COMPRESSION CREEP OF A PULTRUDED E-GLASS/POLYESTER COMPOSITE AT ELEVATED

SERVICE TEMPERATURES

A Thesis Presented to

The Academic Faculty

By

Kevin Jackson Smith

In Partial Fulfillment Of the Requirements for the Degree

Master of Science in Civil Engineering

Georgia Institute of Technology August 2005

COMPRESSION CREEP OF A PULTRUDED E-GLASS/POLYESTER COMPOSITE AT ELEVATED SERVICE

TEMPERATURES

Approved by: Dr. David W. Scott , Chair School of Civil and Environmental Engineering Georgia Institute of Technology Dr. Stanley Lindsey School of Civil and Environmental Engineering Georgia Institute of Technology Dr. Rami Haj-Ali School of Civil and Environmental Engineering Georgia Institute of Technology Date Approved: July 18, 2005

iii

ACKNOWLEDGEMENTS

First, I would like to thank my thesis advisor, Dr. David Scott, for his

immeasurable guidance, wisdom, and patience throughout the duration of this research

program. Without his knowledge and ever-present motivation the work herein would not

have been possible. I would also like to express my gratitude to Dr. Stanley Lindsey and

Dr. Rami Haj-Ali for serving on my thesis committee.

I would also like to sincerely thank my good friend and colleague, Evan Bennett,

for his assistance, insight, and friendship during the course of this work. Without his aid,

many aspects of this study would have been overwhelming. I wish him the best of luck

in the future. I would also like to extend deep gratitude to Melanie Parker for her

assistance and friendship during the course of this work.

In addition, I would like to thank all of my friends who have helped me through

all the hard times along the way. Thanks for reminding me to have a little fun.

Finally, my heartfelt thanks go to my family for their continuous encouragement.

To my sister I would like to express my deepest appreciation for her understanding and

patience. I would like to thank my parents for their guidance and unconditional support

in all of my life’s endeavors.

iv

TABLE OF CONTENTS

ACKNOWLEDGEMENTS iii

LIST OF TABLES vi

LIST OF FIGURES vii

NOMENCLATURE ix

SUMMARY xii

CHAPTER I INTRODUCTION 1

1.1 Scope and Objectives 2

CHAPTER II PREVIOUS WORK 3

2.1 Ambient Temperature Studies 3

2.2 Elevated Temperature Studies 11

CHAPTER III SHORT-TERM TESTING

3.1 Tested Specimens 22

3.2 Characterization of Material Properties 22

3.2.1 Determination of Longitudinal Tensile Properties 23

3.2.2 Determination of Longitudinal Compressive Properties 29

3.2.3 Coupon Test Results 34

3.3 Short-Term Elevated Temperature Tests 38

CHAPTER IV LONG-TERM EXPERIMENTAL PROGRAM

4.1 Introduction 43

4.2 Specimen Details 43

4.3 Long-Term Experimental Setup 46

v

4.4 Development of a Semi-Empirical Viscoelastic Model 57

4.5 Time-Temperature Superposition Principle 72

4.6 Prediction of Time and Temperature Dependent Modulus 84

CHAPTER V CONCLUSIONS AND PROPOSED DESIGN EQUATION

5.1 Conclusions 91

5.2 Proposed Design Equation for the Time and Temperature-Dependent Modulus 93

5.3 Suggestions for Further Research 97

APPENDIX A DESIGN EXAMPLE – LONG-TERM BEAM DEFLECTION 98

APPENDIX B STRESS VS. STRAIN CURVES FROM SHORT-TERM TESTING 102

REFERENCES 128

vi

LIST OF TABLES

Table 2.1 – Test Matrix of Creep Experiments (Yen & Williamson, 1990) 14

Table 3.1 – Nominal Coupon Dimensions 25

Table 3.2 – Measured Coupon Dimensions 35

Table 3.3 – Results of Short-Term Tensile Tests 36

Table 3.4 – Results of Short-Term Compression Tests 37

Table 3.5 – Average Values from Short-Term Testing 38

Table 3.6 – Results of Short-Term Elevated Temperature Tests 42

Table 3.7 – Reduction of Mechanical Properties Due to Temperature 42

Table 4.1 – Nominal Coupon Dimensions for Creep Studies 44

Table 4.2 – Creep Constants m and n from Equation (6) at 0.33 FLc 60

Table 4.3 – Average values for the Material Constant n from Previous Work 60

Table 4.4 – Values for Constants mT and nT 63

Table 4.5 – Initial Elastic Strains 66

Table 4.6 – Increase in Longitudinal Strain over a 50 Year Service Life 71

Table 4.7 – Comparison of Short-Term Strain Values with Creep Values 71

Table 4.8 – Predicted Strains for Material Using Two Methods 79

Table 4.9 – Predicted Strains Utilizing 120 Hour TTSP Curves and Semi-Empirical Model 83

Table 4.10 – Predicted Modulus Reduction for Material at Room Temperature 88

Table 4.11 – Predicted Modulus Reduction for Material at 37.7°C 88

Table 4.12 – Predicted Modulus Reduction for Material at 54.4°C 89

Table 4.l3 – Predicted 50 Year Reduction in Modulus 89

vii

LIST OF FIGURES

Figure 3.1 – Short-Term Coupons 24

Figure 3.2 – Nominal Tensile Coupon Dimensions 26

Figure 3.3 – Short-term Tensile Testing Setup 27

Figure 3.4 – Typical Tensile Coupon Stress-Strain Curve 28

Figure 3.5 – Nominal Compression Coupon Dimensions 31

Figure 3.6 – Nominal Compression Coupon Tested with Extensometer 32

Figure 3.7 – Short-term Compression Test Setup 32

Figure 3.8 – Typical Compression Coupon Stress-Strain Curve 33

Figure 3.9 – Test Setup for Short-Term Elevated Temperature Tests 40

Figure 3.10 – Typical Stress-Strain Curves at Elevated Temperatures 41

Figure 4.1 – Typical Room Temperature Creep Coupon 45

Figure 4.2 – Typical Elevated Temperature Creep Coupon 45

Figure 4.3 – Schematic of Creep Fixture (from Scott and Zureick (1998)) 47

Figure 4.4 – Typical Compression Cage (from Scott and Zureick (1998)) 48

Figure 4.5A – Creep Fixture with Environmental Chamber 49

Figure 4.5B – Room Temperature Creep Fixture 49

Figure 4.6 – Creep Fixture with Applied Dead Load 52

Figure 4.7 – Creep Strains for Coupons at Room Temp. 23.3°C (74°F) and 0.33 FL

c 53 Figure 4.8 – Creep Strains for Coupons at 37.7°C (100°F) and 0.33 FL

c 54 Figure 4.9 – Creep Strains for Coupons at 54.4°C (130°F) and 0.33 FL

c 55

Figure 4.10 – Creep Strains for Coupons under Cyclic Heating at 37.7°C (100°F) and 0.33 FL

c 56

viii

Figure 4.11 – Logarithmic Plot for Evaluation of Constants m and n at 23.3°C 59

Figure 4.12 – Plot of Creep Strain at Elevated Temp., minus Creep Strain Measured at Room Temp. 62 Figure 4.13 – Logarithmic Plot of Creep Strain at Elevated Temp., minus Creep Strain Measured at Room Temp. 63 Figure 4.14 – Experimental Creep Strain with Time/Temperature-Dependent Model 65

Figure 4.15 – 37.7°C Cyclic Heat Creep Strains with Power Law Model 67

Figure 4.16 – Predicted Strains over a 50 Year Service Life 70

Figure 4.17 – Creep Strain for Temperature of 23.3°C, 37.7°C, and 54.4°C 73

Figure 4.18 –Master Curve Including Shift of 37.7°C Curve 75

Figure 4.19 –Master Curve for To (23.3°C) Including Shifts of Creep Data at 37.7°C and 54.4°C 76 Figure 4.20 – Shift Factors for TTSP 77

Figure 4.21 – Master Curve for To (37.7°C) Including Shift of Creep Data at 54.4°C 78

Figure 4.22 - Recorded Creep Strain for 120 hours 81 Figure 4.23 - TTSP Master Curve for Test Durations of 120 Hours, Allowing Prediction of Strain Response over a 50 Year Service Life 82 Figure 4.24 – Evaluation of Creep Parameter m’ and To 85

Figure 4.25 – Predicted Reduction in Modulus of Elasticity Over a 50 Year Service Life 90

Figure 5.1 – Reduction in Modulus with Simplified Design Equation 96

Figure A1 – Beam Deflection Example 99

ix

NOMENCLATURE

aT shift factor

D(t) total time-dependent creep compliance

Do instantaneous creep compliance

Dt transient creep compliance

EL longitudinal elastic modulus EL

c longitudinal elastic compression modulus from coupon tests

ELt longitudinal elastic tensile modulus from coupon tests

ELo initial elastic longitudinal modulus independent of time

EL(t) time-dependent longitudinal elastic modulus

EL(T) temperature-dependent longitudinal elastic modulus

EL(T,t) time-dependent and temperature-dependent longitudinal elastic modulus

Et modulus which characterizes only the time-dependent behavior

ET modulus which characterizes only the temperature-dependent behavior

f applied stress

FLc longitudinal elastic ultimate compressive stress from coupon tests

FLt longitudinal elastic ultimate tensile stress from coupon tests

g2 non-linearizing material parameters in the Schapery equation

GLT elastic inplane shear modulus

I moment of inertia

lg coupon gage length

L length

m stress-dependent and temperature-dependent coefficient

x

m’ stress-dependent and temperature-dependent coefficient

mRT stress-dependent coefficient from room temperature creep test

mT stress-dependent and temperature-dependent coefficient from elevated temperature tests

n stress-independent material constant

nRT stress-independent material constant from room temperature creep test

nT stress-independent material constant from elevated temperature test

t time after loading

T temperature

To creep material parameter used in the hyperbolic form of the coefficient of

the temperature-dependent portion of strain in Findley’s power law

equation

Vf the volume fraction of reinforcing fibers

β: ratio of creep modulus to initial elastic modulus

Δ beam deflection

Δo initial beam deflection

Δ(T,t) beam deflection due to time and temperature effects

ΔE(T) reduction in modulus due to temperature

ΔE(t) reduction in modulus due to time

ΔT difference between given T and the material constant To

ε total elastic strain

xi

εT strain due to temperature

εt strain due to stress and time

ε(t) total time-dependent creep strain

ε(T) total temperature-dependent creep strain

ε(T,t) total time-dependent and temperature dependent creep strain

εo stress-dependent initial elastic strain

)(tφ modulus reduction factor for time

),( tTφ modulus reduction factor for time and temperature

ζ “reduced time”

xii

SUMMARY

This thesis presents the results of an experimental investigation into the behavior

of a pultruded E-glass/polyester fiber reinforced polymer (FRP) composite under

sustained loads at elevated temperatures in the range of those that might be seen in

service. This investigation involved compression creep tests of material coupons

performed at a constant stress level of 33% of ultimate strength and three temperatures

levels; 23.3°C (74°F), 37.7°F (100°F), and 54.4°C (130°F). The results of these

experiments were used in conjunction with the Findley power law and the Time-

Temperature Superposition Principle (TTSP) to formulate a predictive curve for the long-

term creep behavior of these pultruded sections. Further experiments were performed to

investigate the effects of thermal cycles in order to better simulate service conditions.

1

CHAPTER I

INTRODUCTION

Fiber reinforced polymeric (FRP) composite materials are rapidly becoming state

of practice in many civil engineering construction applications. These materials often

display many useful characteristics when compared with traditional building materials

such as structural steel or reinforced concrete. Depending on the constitutive materials

used, those characteristics can include corrosion resistance, high strength to weight ratio

and non-conductivity. Another characteristic of FRP materials is a large degree of

adaptability to a particular design situation. The mechanical properties of FRP materials

can be altered by manipulating the type of fiber, the type of resin, the fiber volume

fraction, and most importantly, the fiber orientation.

One of the more popular and cost efficient methods of producing FRP sections is

the pultrusion process. The pultrusion process takes continuous fibers and pulls them

through a resin bath and then through a heated die where the desired shape is formed and

the polymerization of the resin occurs. The pultrusion process offers the ability to

construct many of the same shapes that are typically found with other construction

materials such as I-shapes, channels, bars, angles, tees, and tubular sections.

While FRP plates and sheets have been used for many years to strengthen existing

structures (ACI 440 (1996)), the lack of reliable design criteria for FRP structural

sections has slowed the acceptance of these materials by practicing engineers. One of the

major hurdles to the development of reliable design criteria is a lack of understanding of

the behavior of FRP materials under sustained loading. In addition, the types of FRP

materials proposed for use in civil applications have shown a much greater sensitivity to

2

temperature variations than traditional construction materials. At elevated temperatures

the resin matrix softens, which ultimately decreases ultimate strength and the modulus of

elasticity. A reliable methodology to assess how these mechanical properties are

diminished due to elevated temperatures is needed in order to develop more accurate

predictive models of structural behavior over a normal service life.

1.1 Scopes and Objectives

This thesis presents the results of an experimental investigation into the behavior

of a pultruded E-glass/polyester fiber reinforced polymer (FRP) composite under

sustained loads at elevated temperatures in the range of those that might be seen in

service. This investigation involved compression creep tests of material coupons

performed at a constant stress level of 33% of ultimate strength and three temperatures

levels; 23.3°C (74°F), 37.7°F (100°F), and 54.4°C (130°F). The results of these

experiments were used in conjunction with the Findley power law and the Time-

Temperature Superposition Principle (TTSP) to formulate a predictive curve for the long-

term creep behavior of these pultruded sections. Further experiments were performed to

investigate the effects of thermal cycles in order to better simulate service conditions.

3

CHAPTER II

PREVIOUS WORK

A large body of work currently exists on the time-dependent behavior of FRP

composite materials. This chapter surveys those investigations deemed pertinent to the

current study. An extensive survey of existing technical literature concerning creep

behavior of FRP composites has previously been presented by Scott, Lai, and Zureick

(1995). The current study reviewed a number of investigations pertaining to the creep of

various FRP composites, the influence of elevated temperatures on creep behavior, and

the techniques employed to model the creep behavior.

2.1 Ambient Temperature Studies

Findley (1944) formulated a power law equation to fit creep curves of various

plastics previously tested by the author. The simplest form of the equation takes the

form:

no mtt += εε )( (2.1)

The recorded strain from creep tests can be plotted versus time on a log-log scale. The

value of the power n can be determined by measuring the slope of the resulting line. The

value of coefficient m can be determined as the y-intercept of the line at t = 1 hour. The

material constant n was determined to be independent of stress while m is stress

dependent. A 17,000 hour creep test of cellulose acetate was accurately modeled using

the power law under low stresses. The author asserted from the various materials tested

that as the modulus of elasticity decreased the resistance to creep also decreased. The

4

author concluded that the power law equation permitted reliable extrapolation of the data

past the duration of available tests.

Spence (1990) tested a unidirectional glass/epoxy composite rod loaded to 30% of

ultimate compressive strength. The specimen was tested at 21°C (70°F) and 207 MPa

(30 ksi). The test specimen was a pultruded rod with a 0.635 cm (0.25 inch) diameter and

a length of 1.90 cm (0.75 inch). The specimen consisted of S2 glass roving in an epoxy

resin matrix. The fiber volume of the specimen was approximately 60%. The elastic

modulus of the material was 41 GPa (5947 ksi), and the ultimate strength of 689 MPa

(100 ksi). A constant load of 6.67 kN (1.5 kips) was placed on the specimen for 840

hours. After the loading period was over the specimen was then measured again to

calculate the total deformation. The axial strain measured in the rod at the end of the test

was found to be 0.04%.

The data was then extrapolated to 100,000 hours (10 years). Extrapolation of the

data was carried out using the creep correlation method. The authors concluded that

unidirectional composites are capable of sustaining stresses of 30% of ultimate while

maintaining geometric stability.

Gibson et al (1991) characterized the creep behavior of glass/pps composites

using the Frequency-Time Transformation (FTT) of frequency domain hysteresis loop

measurements. These tests were performed in both wet and dry conditions in a servo-

hydraulic testing machine. The specimens were comprised of 24 ply symmetric glass/pps

laminates and were machined to the dimensions outlined in ASTM D-695. The

specimens were subjected to a 100 pound pre-load and cyclic loading of +/- 80 pounds.

This load range produced a very small strain and ensured linearity of the measurements.

5

The complex modulus was determined from the load-strain hysteresis loop

measurements. The resulting compressive complex moduli were then transformed to the

time domain compressive creep compliance using FTT method. This method was

introduced as an alternative to the Time Temperature Superposition Principle (TTSP)

which uses aggressive environmental conditions to accelerate the testing process. The

aggressive elevated temperatures that are needed in order to use the TTSP can cause

physical aging of the material which can cause a non-linear viscoelastic response of the

material. This non-linearity can cause incorrect predictions of isothermal creep response

of the material. The authors assert that the FTT method eliminates this non-linearity.

Five compression creep tests were performed in order to compare the results of

FTT and actual creep response. Creep tests were performed for 4.636x106 seconds (1287

hrs). The FTT creep compliance curve, which is denoted as J(t) = ( ε(t) / σ0), had good

agreement with the actual creep tests which were slightly higher. As expected, the curves

had better agreement at a time period less than 105 seconds. The authors assert that the

FTT method is an efficient way of characterizing the creep behavior of composite

materials without subjecting the material to aggressive climates.

McClure and Mohammadi (1995) investigated the creep behavior of three

pultruded-angle FRP sections, reinforced with E-glass. The material was found to

contain a fiber volume fraction Vf of 35-45%. The creep fixtures for this study utilized a

cantilever arm device used to multiply the dead load applied to the end by a factor of 10.

The same apparatus was used in the coupon and angle stub creep tests. The angle stub

creep specimens were cut to dimensions of 152.4 mm (6 in.) in length and cross-sectional

dimensions of 50.8 mm (2 in.) x 50.8 mm (2 in.) x 6.35 mm (0.25 in.). The specimens

6

were equipped with 12 strain gages (3 on each face). The stubs were subjected to a load

of 23.2 kN (5.2 kips) after the cantilever action which corresponds to a stress of 44 MPa

(18.26 ksi) which is approximately 45% of the initial buckling load. The coupon

specimens used had cross-sectional dimensions of 12.7 mm (0.5 in.) x 6.35 mm (0.25 in.)

and a length of 31.75 mm (1.25 in.). The coupons were equipped with two strain gages

(one on each face). All of the specimens were cut from the stronger of the two legs of the

single angle which was found to be leg number 1. The coupons were subjected to a stress

of 146 MPa (21.2 ksi), approximately 45% of the average ultimate stress of the

composite.

The Findley power law was used to model the time-dependent behavior of the

material. Interestingly, the material constant n was not consistent for the two different

tests. This was not desirable because Findley’s theory defines n as a material constant

independent of stress and environmental conditions. Further testing was suggested by the

authors in order to assess the difference in n.

Still, the authors concluded that the Findley power law was an effective model of

the creep behavior of the GFRP material. Notably, this model does not effectively model

nonlinear tertiary creep; therefore the stress level must remain relatively low. Using the

power law model, it was asserted that a full-sized structural element would only creep 0.3

mm after a 2,500 hour period. This was deemed acceptable from a civil engineering

design perspective.

Wen, Gibson, and Sullivan (1995) utilized dynamic testing methods to

characterize the creep behavior of polymer composites. The study used impulsive

excitation of the specimens and their frequency response to determine the frequency

7

dependent storage modulus and loss factors. The Time-Temperature Superposition

principle was applied to the frequency domain vibration test data to form a master curve.

This curve was then transformed to the time domain to generate the creep compliance

curve. The purpose of this study was to compare the results of the short term dynamic

test method to the results of conventional long term static creep tests. The technique used

by the authors is known as the impulse-frequency response technique. The authors

asserted that it was known to work well in materials in their glassy state. Polyetherimide

(PEI) neat resin and E-glass/PEI composites (Vf = 35%) were selected as the material for

this study. The material was cut into specimens that were 15cm in length by 1.27cm in

width. The glass transition temperature of the material was estimated to be around 210°-

215°C. Aging effects were eliminated by rejuvenating the specimens at 225°C for 3

hours. The authors concluded that the vibration tests could be used to predict creep

compliance for a short amount of time, on the order of seconds, while creep tests showed

longer periods; however, the time overlap show good correlation between the two

methods. The authors emphasized that the preparation time and setup cost is much less

for the vibration test than conventional creep tests.

Scott and Zureick (1998) investigated the compression creep of pultruded FRP

composites at three different stress levels and time durations of up to 10, 000 hrs.

Rectangular coupons were cut from the structural plate elements of a 102 mm (4 in.) x

102 mm (4 in.) x 6·4mm (.25 in.) pultruded FRP wide flange section. The material

system consisted of a vinylester matrix reinforced with unidirectional E-glass roving and

continuous filament mat. The fiber volume fraction was found to be 30% with a filler

content of approximately 5% by volume.

8

The specimens were loaded using a lever arm creep fixture and concrete weights.

Stress levels of 65 MPa (9.43 ksi), 129 MPa (18.7 ksi), and 194 MPa (28.1 ksi) were

applied to the specimens. This corresponded to 20%, 40%, and 60% of the average

ultimate compressive strength respectively. The stress levels of 20% and 40% are well

within the linear-elastic range found in the short-term tests. The stress level of 60% is

approximately where the material began to display non-linear behavior.

The data was modeled using the Findley power law. The model that was

developed by Findley was based on an unreinforced thermoplastic material. Since the

composite in this study possessed a low fiber volume fraction of 30%, the authors

asserted that the creep behavior would be primarily matrix driven and therefore the

Findley model would be an accurate approximation.

A predictive equation for the time-dependent elastic modulus was developed

using a Taylor series expansion of the stress dependent terms εo and m. These terms can

be expressed as hyperbolic functions of stress. The equation was simplified because the

creep parameters are approximated as linear functions of stress so the cubic and higher

terms in the Taylor series were neglected. This approximation may not be valid for

higher stress levels where the relationship is no longer linear. The predictive equation

proposed by Scott & Zureick was

oLt

oL

oL

n

t

oL

oL

L Et

E

t

E

tEEEtE φ

ββ

=+

≈+

=+

=25.025.0

25.0 101)8760(11)( (2.2)

where

25.0101

1

tt

β

φ+

= (2.3)

9

and β = oL

t

EE . The property Et is the modulus that characterizes the time dependent

behavior given by mf which is the applied stress divided by the material parameter m.

The property ELo is the initial longitudinal elastic modulus of the material.

The predictive model showed a 28% reduction in longitudinal stiffness over a 75

year period. The predicted reduction in stiffness was not stress dependent. Thus the

authors recommended that the sustained stress level remain under 33% of the ultimate

stress to ensure that the Findley model provides an accurate model of the material

behavior.

Papanicolaou, Zaoutsos, Cardon (1999) investigated the well-known Schapery

formulation which models the non-linear viscoelastic response of any material using four

stress and temperature dependent parameters and estimated them for FRP material using

simple step creep-recovery curves. Previous research by Papanicolaou, Zaoutsos, Cardon

(1998) predicted three out of the four parameters using step creep-recovery curves. In the

later investigation the authors estimated the fourth nonlinear parameter, which accounts

for the influence of the loading rate on creep, and depends on stress and temperature.

The fourth parameter was found using a new methodology developed by the authors

which is based on the Schapery model and assumes the material time-dependent

compliance follows a power law.

Creep recovery data was obtained on unidirectional carbon-epoxy composite

plates. The specimens were constructed using the hand lay-up technique with 12 plies in

each. The specimens were 300mm (11.8 in.) in length, 17mm (0.67 in.) wide and 2mm

(0.079 in.) thick. Short term tensile elastic modulus and ultimate tensile strength tests

10

were performed for five specimens. For the long-term loading the initial applied stress

remained constant for 168 hrs followed by 168 hrs of recovery time. Six different stress

levels were investigated: 30%, 40%, 50%, 55%, 60%, and 70% of the tensile rupture

stress. The CF/Epoxy composite displayed strong viscoelastic behavior and was

dominated by the matrix. The composite displayed a nonlinear viscoelastic strain

response for applied stresses higher than 30% of the ultimate strength. Using the new

methodology the authors asserted that the fourth parameter g2 increased with increasing

stress levels.

Haj-Ali and Muliana (2003) presented a new three-dimensional modeling

approach to predict the non-linear viscoelastic behavior of pultruded composites. The

material that was investigated consisted of a vinylester matrix reinforced with E-glass

roving and a continuous filament mat (CFM) with an overall Vf of 34%.

Micromechanical models, utilizing finite element, were formulated for the roving and

CFM. A new iterative integration method applied to the Schapery three-dimensional

model was used for the isotropic matrix. The matrix in both models had the same

isotropic and nonlinear viscoelastic behavior. The fibers were taken as linearly elastic.

Uniaxial compression creep tests were performed on off-axis coupons at angles of

0, 45, and 90 degrees at room temperature for 1 hour. The coupons used for the creep

tests were 177.8 mm (7 in.) in length x 31.75 mm (1.25 in.) x 12.7 mm (0.5 in.) thick.

Multiple stress levels ranging from 10-60% of the ultimate strength of the material were

used for the creep experiments. The short duration creep tests were used to calibrate the

viscoelastic properties of the matrix and to assess the prediction capabilities of the

models. The linear coefficients were determined from creep tests with low magnitudes of

11

applied stress. The nonlinear parameters of the Schapery model were calibrated based on

the tests at the elevated stress levels. The authors asserted that the micromodels showed

good prediction for all the linear and nonlinear curves except for the highest stress level.

This was attributed to the calibration being based on a lower applied stress. The authors

concluded that the nonlinear response was apparent in the off-axis creep tests and that the

micromodel predictions produced a good match.

2.2 Elevated Temperature Studies

Findley and Worley (1951) investigated elevated temperature creep and fatigue

properties of a polyester glass fabric laminate. The material was a glass fabric laminated

with a polyester resin. The high temperature creep tests were conducted in a commercial

creep testing machine. The specimens were tested at 25°C (77°F) and 204°C (400°F).

The specimens were allowed to remain at temperature from 1 to 24 hours before the

application of the load. Stress levels of 103.4 MPa (15,000 psi), 137.9 MPa (20,000 psi),

and 172.4 MPa (25,000 psi) were tested at the elevated temperature. The 137.9 MPa

(20,000 psi) test was continued as a step test to determine the stress level where fracture

could be expected. The stress level was increased by 13.8 MPa (2,000 psi); fracture of

the specimen occurred when the stress reached 179.3 MPa (26,000 psi). A test was also

performed at a stress level of zero to determine the shrinkage at elevated temperature.

The test at the zero stress level showed significant shrinkage which would alter

the creep curves if this adjustment was taken into account. The results indicated that the

stiffness of the laminate increased with the duration of exposure to the elevated

temperature. This was due to a change in the structure of the material due to post-cure

effects. The data showed a 30 percent increase from an exposure of 16 hours to 262

12

hours. The authors concluded that the specimens must be exposed for the same amount

of time if the results were to be comparable. The authors asserted that the strain at

elevated temperatures is not only affected by temperature and stress but also shrinkage

and stiffening of specimen.

Tuttle and Brinson (1986) investigated the prediction of the long-term creep

compliance of general composite laminates using the Schapery non-linear viscoelastic

theory. Specimens with 0, 45, and 90° fiber orientations were cut from 8-ply

unidirectional panels of T300/5208 carbon epoxy composite. The fiber volume fraction

of the material was found to be 65%. The specimens were cut to dimensions of 13 mm

(0.51 in.) in width and the length ranged from 180 – 330 mm (7 – 13 in.). The thickness

was 1 mm (0.04 in.). Short-term creep/creep recovery tests were performed on a creep

machine with automatic loading with a lever arm amplification of 3:1. All tests were

performed at 149°C (300°F). The creep portion of the test was 480 minutes and the

recovery time was 120 minutes. These times were selected in order for the creep

compliance to be accurate at times up to 105 minutes. The viscoelastic parameters in the

Schapery equation were determined through a least-squares fit using the experimental

data.

Five specimens were used for the long-term creep tests. The tests were performed

at a stress level of 76 MPa (11,022 psi) and a temperature of 149°C (300°F). The tests

were performed for a duration of 105 minutes. Comparison of the creep data with the

Schapery prediction yielded reasonably accurate results up to a time period of 103

minutes. Predictions after 103 minutes fell below the measured values. The predicted

response at 105 minutes fell 10-15 percent below the measured values. The authors

13

attributed the error to incorrect modeling of bi-axial stress interactions and damage

accumulation within the plies.

Yen and Williamson (1990) tested creep and creep recovery of a unidirectional

off-axis FRP composite that contained 50% by weight of continuous glass fiber in a

polyester resin matrix. The composite had a fiber orientation of 15° with respect to the

direction of the applied load. The specimens were cut into sections 203mm (8 in.) long

and 12.7mm (0.5 in.) wide. The glass transition temperature for this material was

reported to be 135°C (275°F). The ultimate stress at temperatures of 23°C (73.4°F),

38°C (100.4°F), 66°C (150.8°F), 93°C (199.4°F), 121°C (249.8°F), and 149°C (300.2°F)

was determined through tensile testing of the material.

The test matrix for the creep experiments can be seen in Table 2.1. The different

stress levels represented percentages of the average ultimate strength. The tests were

conducted on a five-lever arm creep frame and each lever arm of the creep frame was

equipped with an oven and temperature controller. Each test ran for a duration of 180

minutes with approximately 15 hours of recovery. According to the test matrix and the

given glass transition temperature, samples were tested in the both the glassy and rubbery

phases of the material. The authors asserted that the response of the material, at all

temperatures, would be in the glassy state because of the presence of the fibers.

14

Table 2.1: Test Matrix of Creep Experiments (Yen & Williamson, 1990)

Stress Level (MPa) Temperature (°C)

23 52 79 107 135 149 5.4 X 7.6 X 9.0 X 10.8 X X X X 12.7 X X 16.3 X X 17.6 X 18.0 X 21.5 X 22.7 X 32.3 X X X X 36.5 X 42.1 X 53.8 X X X 75.4 X 96.5 X

The collected data was modeled using the Findley equation along with the Time-

Temperature-Stress Superposition principle to create master curves to model the long-

term creep response. Curves were created for 57 days and 400 days based on the

aforementioned 180 min short-term creep tests. The measured strain response was used

to estimate the parameters in the Findley equation. Creep data showed very small

deviation from the results of the Findley equation.

The time exponent, n, was found to have little variation with a change in the

stress which is concurrent with Findley’s observations that n is stress independent. The

test data showed that n increased non-linearly with temperature which conflicts with

15

Findley’s findings that n is almost independent of temperature. The value of εo showed a

non-linear increase with stress; however, the rate of increase was found to decline as the

stress increased. The value of m showed an increase with both temperature and stress

level. Master curves were found using horizontal and vertical shift factors on the data

collected at different temperatures and relating them to the reference temperature. The

authors asserted that a 28 hour creep test at 149°C (300°F) could be use to predict the 10-

year creep response for the material.

The authors stressed that this duration of testing does not take into account the

physical aging of the specimen which can change the creep response of a material. The

authors suggested longer testing periods in order for the aging effect to be included. The

maximum error that was found between the master curve and the Findley equation was

5%. The accelerated tests make it possible to predict the response of the material up to

3200 times the duration of the original test.

Gates (1993) investigated two types of FRP material to establish non-linear time-

dependent relationships for stress/strain over a range of temperatures. The first material

system was comprised of an amorphous graphite/thermoplastic composed of Hercules®

IM7fiber and Amoco® 8320 matrix. The second FRP was a graphite/bismaleimide

composed of Hercules® IM7 fibers and Narmco® 5260 matrix. Both specimens had a

glass transition temperature of 220°C (428°F). The constitutive model that was

developed accounted for temperature dependency through the variation of material

properties with respect to temperature. The model would therefore be applicable to both

tensile and compressive loading. The model was designed to predict the non-linear rate-

dependent behavior such as creep.

16

The six temperatures selected for the study were 23°C (73.4°F), 70°C (158°F),

125°C (257°F), 150°C (302°F), 175°C (347°F), and 200°C (392°F). Rectangular test

specimens were cut following ASTM D3039-76 which consisted of 12 plys measuring

2.54 cm (1 in.) by 24.1 cm (9.5 in.). Elastic material constants were determined on

specimens 0, +/-45, and 90 degree orientations in order to determine the elastic modulus

and the shear modulus of the material. For the three elastic/plastic and two

elastic/viscoplastic material parameters, off-axis tests were performed on 15, 30, and 40

degree coupons.

The trends of the different temperature tests showed that transverse and shear

moduli stiffness decreased with increased temperature. Both materials displayed an

increase in ductility as the temperature increased. The authors found the results indicated

that the analytical model provided reasonable predictions of material behavior in load or

strain controlled tests.

Katouzian and Bruller (1995) investigated the effect of temperature on the creep

behavior of neat and carbon fiber-reinforced PEEK and epoxy resins. Two composite

materials were used in this investigation. One was an epoxy resin matrix reinforced with

T800 carbon fibers and the other was a semi-crystalline PEEK matrix reinforced with

IM6 carbon fibers. The fiber volume for each of the composites tested was

approximately 60%. The neat resin matrices for each composite were also tested.

Creep experiments were performed in creep fixtures utilizing lever arm action

with force amplifications of 10:1 and 25:1. Dead weights acting at the ends of the lever

arms generated the tensile force needed for the experiments. The high temperature tests

were performed in thermostatically controlled chambers. The creep specimens used in

17

the experiments had a length of 150 mm (5.9 in.), a width of 10 mm (0.394 in.), and a

thickness of 1 mm (0.039 in.). Fiberglass end tabs were used on all specimens. The test

duration for all creep tests was 10 hours.

The temperatures tested for the neat PEEK matrix were 23°C (73.4°F), 60°C

(140°F), 80°C (176°F), and 100°C (212°F) while the reinforced material was tested at

23°C (73.4°F), 80°C (176°F), 100°C (212°F), and 120°C (248°F). The neat and

reinforced epoxy materials were tested at 23°C (73.4°F), 80°C (176°F), 120°C (248°F)

and 140°C (284°F). The room temperature (23°C (73.4°F)) tests were conducted at five

stress levels ranging between 10 and 70% of the ultimate tensile strength. The load levels

were reduced with increasing test temperature. The test specimens were allowed to cure

at the test temperature to ensure even heat distribution throughout the specimens.

The authors used the well known Schapery equation to model the results of the

creep experiments. It was discovered that the linear viscoelastic limit shifted to lower

values with increasing temperature for the neat epoxy and reinforced epoxy. It was also

found that the instantaneous creep response is far less sensitive to temperature than the

transient response. The instantaneous creep response showed slight increases with

increasing temperature and was found to be linear up to stress levels of 20 MPa (2,900

psi) for the epoxy resin and reinforced epoxy. The transient creep response showed a

nonlinear dependence of temperature. The transient creep response showed very little

influence from temperature between 23°C (73.4°F) and 80°C (176°F) but increases to

140°C (284°F) showed significant effects for the neat epoxy and reinforced epoxy. A

comparison between the two resins showed that the influence of temperature on the creep

response in the PEEK resin was greater than the epoxy resin. The results of the PEEK

18

resin showed that the linear viscoelastic limit shifted to lower values with increasing

temperature. This was not evident in the reinforced PEEK resin where the linear limit

was approximately 25 MPa (3,625 psi) for all tests.

The authors asserted that the Schapery approach provided a good approximation

of the experimental results with a maximum error of less than 3%. The authors also

stated that the instantaneous response is linear and temperature-independent over the

stress levels used in practical applications. Finally, the authors claimed that the influence

of temperature on the time-dependent response of the materials was found to be

nonlinear.

Raghavan and Meshii (1997) presented a model to predict creep of unidirectional,

continuous carbon-fiber-reinforced polymer composite and its epoxy matrix. Creep was

studied over a wide range of stress levels (10-80%) and temperatures ranging from 295K

(71.3°F) to 433 K (319.7°F).

Laminates were made in house in an autoclave. Eight plies were used for the 0,

10, 30, and 60 degree laminates. Sixteen plies were used for the 90 degree laminates.

The fiber volume fraction was 62%. The 0, 10, and 90 degree laminates were used to

measure longitudinal, shear and transverse properties. The 30 and 60 degree laminates

were used in the creep testing. Tensile test coupons 167 mm in length and 12.7 mm in

width were used. The coupon dimensions were based on the measurements provided by

ASTM D638M-96 (1996). Thermal activation energy was used to model the behavior of

the material. This was used as opposed to the time-temperature-stress superposition

principle (TTSSP) because it can be used to model non-linear viscoelastic materials.

19

The four temperatures that were tested were 295K (71.3°F), 373K (211.7°F),

403K (265.7°F), and 433K (319.7°F). Creep experiments were performed for a

maximum duration of 24hrs. Three moduli were calculated from short term tests. They

were the instantaneous modulus, the rubbery modulus and the viscous modulus. These

represented the modulus with respect to the temperature which the specimen was being

tested. The authors asserted that the model provided good correlation with the creep data

for the unidirectional composite for the temperature range that was tested and stress

levels up to 80% of the ultimate strength. The model showed reasonable quantitative

agreement with predicted results being higher by 15 – 23%.

Bradley et. al. (1998) investigated creep characteristics of neat thermosets and

thermosets reinforced with E-glass. Vinylester samples were machined to dimensions of

1.27 cm (0.5 in.) wide by 10.2cm (4.02 in.) long and 0.318 cm (0.125 in.) thick. The

specimens were tested in flexural creep and displacements were measured using dial

gages. The specimens were post-cured at temperatures of 48.9°C (120°F), 71.1°C

(160°F), and 93.3°C (200°F) for time durations of 2 and 4 hours. The purpose of the

experiments was to determine the effect of temperature and time of cure on the creep

compliance of the materials. Loading and unloading of the specimens was performed in

order to determine the initial creep compliance Do.

The creep data was modeled using a form of the Findley equation taking the form:

nto tDDttD +==

σε )()( (2.2)

where

D(t) = total time-dependent creep compliance ε(t) = total time-dependent creep strain σ = applied stress

20

Do = instantaneous creep compliance Dt = transient creep compliance t = load time n = stress –independent material constant The authors observed that an increase in curing temperature resulted in a reduction in the

creep compliance as well as a reduction in the time exponent n.

Saadatmanesh (1999) investigated the long-term behavior of plastic tendons

reinforced with aramid fibers. The Aramid Fiber Reinforced Plastic (AFRP) tendons had

a fiber volume fraction of 50% with a filament diameter of .012mm (0.00047 in.). Five

specimens were tested until failure to evaluate the mechanical properties. The short-term

testing resulted in a tensile strength of 91.2kN (20.5 kips), an ultimate stress of 2324 MPa

(337 ksi), and an ultimate strain of 2.1%. The modulus of elasticity of the AFRP tendons

was 120.7 GPa (17,500 ksi) with a Poisson’s of 0.36. The average diameter of the

tendon was 10mm (0.39 in.) and across-sectional area of 78.5 mm2 (0.12 in.2). Twelve

specimens were tested in air temperatures of -30°C (-86°F), 25°C (77°F), and 60°C

140°F), and 24 specimens were tested in alkaline, acidic, and salt solutions at

temperatures of 25°C (77°F) and 60°C (160°F) to evaluate the relaxation behavior. Six

specimens were tested under sustained load to evaluate creep at room temperature, and 45

specimens were tested to evaluate fatigue behavior.

The creep investigation was just a preliminary investigation. Samples were

subjected to a load of 40% of ultimate load. The average initial strains were 0.82, 0.84,

and 0.83 percent creep for samples in air, alkaline solution, and acidic solution. The

specimens were put into tension using a hanging dead weight to create the stress on the

specimens. The specimens were subjected to the load for up to 3000 hrs and the strains

were recorded on one hour intervals. The author asserted that the specimens exhibited

21

good creep characteristics in air and alkaline solutions and to a lesser degree in acidic

solutions.

Dutta and Hui (2000) asserted that the behavior of FRP material at elevated

temperatures is essential for assessing the survival time of a structure undergoing a fire.

The purpose of this study was to develop engineering constants that can be used as

material parameters, allowing for the assessment of heat durability. The strength

degradation and final collapse of FRP structures due to the increase in temperature in a

fire was investigated. An isothermal curve can be created by running a simple creep test

at constant stress and temperature while recording the strain.

The time-temperature superposition principle was decided against because it was

too complex and did not meet the desired simplified method. The method that was

decided upon was an adaptation of the Findley equation.

Short-term tests were performed at room temperature (25°C (77°F)) in order to

establish mechanical properties of the FRP. The specimens were then tested at sustained

loads in the range of 60-80% of ultimate load at 25°C (77°F), 50°C (122°F), and 80°C

(176°F). The failure mode was semi-brittle. The average failure strength at 25°C (77°F)

was 304.4 MPa (44.1 ksi) in compression and 271.5 MPa (39.4 ksi) in tension. The 25°C

(77°F) specimens continued to strain under creep loads for over 30 min. The 50°C

(122°F) and 80°C (176°F) specimens were tested until failure because they typically

broke before the 30 minute test period. A semi-empirical equation was developed using

Findley’s power law. The two creep constants were replaced with functions of time

ratios and temperature ratios. The resulting equation was compared with data collected in

this experiment and experiments performed by other researchers, with good agreement.

22

CHAPTER III

SHORT-TERM TESTING

3.1 Tested Specimens

All tested specimens in the current investigation were manufactured using an

isophthalic polyester resin matrix containing UV radiation inhibitors reinforced with

unidirectional E-glass roving and a continuous filament mat. Specimens were cut from

101.6 mm (4 in.) wide square tube structural elements with a wall thickness of 6.35 mm

(0.25 in.). Results from previous work indicated that the fiber volume fraction for the

material is approximately 35%, with 9% filler and 1.7% voids by volume (Kang, 2001).

3.2 Characterization of Elastic Material Properties

Short-term tests were conducted in both compression and tension in order to

determine modulus of elasticity, ultimate strength, and ultimate strain of the material.

The results of the short-term tests were used to set the parameters for the long-term

experiments. The specimens were tested in both compression and in tension to ensure the

composite performed the same in both loading conditions. The specimens in the

following tables will be designated by resin type, reinforcement type, test type, specimen,

section designator, and panel number. For example, PGT-A1-1, would denote Polyester,

Glass, Tension, square tube A, section 1, panel number 1.

Short-term material properties were investigated for each panel of the structural

members that were to be used in the long-term investigation. This was done to ensure all

of the structural members were similar and did not contain discontinuities that could

cause premature failure when tested in the long-term.

23

3.2.1 Determination of Longitudinal Tensile Properties

A total of 16 uniaxial tension tests were performed in order to determine the

longitudinal tensile properties of the square tube sections used in this study. Three

different square tube sections were used, with a specimen being cut from each of the four

panels as shown in Figure 3.1. Two sections were cut from specimen A to confirm the

accuracy and repeatability of the test results. All longitudinal tension tests were

performed using a hydraulic testing machine with pneumatic grips. Coupon preparation,

loading procedure and data reduction were performed in accordance with ASTM D3039

(1993).

Guided by previous work by Butz (1997) and Kang (2001) the tensile properties

were determined using prismatic coupons without end tabs. The nominal dimensions for

the tensile coupons used in the current study are given in Table 3.1. A schematic of the

coupons used in the short-term tensile tests can be found in Figure 3.2. The gage length

of the tensile coupons was 203 mm (8 in.) with approximately 127 mm (5 in.) being

added to guarantee adequate seating in the pneumatic grips. A single uniaxial

extensometer was used to measure the longitudinal strain in the coupon. The

extensometer was removed at a predetermined stress of 241MPa (35,000 psi) to prevent

damage to the extensometer. Due to the absence of the extensometer for the remainder of

the test, strain at failure was estimated based on an assumed linearity of the stress-strain

response of the composite material. A photograph of the short-term tensile test setup

can be found in Figure 3.3. A typical stress-strain diagram for the short-term coupon

tests can be found in Figure 3.4 and all others can be found in Appendix B.

24

L g

TYPICAL COUPON

ROVING DIRECTION

b

L

t

Figure 3.1 – Short-Term Coupons

25

Table 3.1- Nominal Coupon Dimensions

Test Type t L Lg b

mm in. mm in. mm in. mm in.

Tension 6.35 0.25 330 13 203 8 25 0.984

Compression 6.35 0.25 127 5 51 2 25 0.984

Compression (Strain

Readings) 6.35 0.25 127 5 51 2 38 1.5

26

25 mm

6.35 mm

330 mm

203 mm

Figure 3.2 - Nominal Tensile Coupon Dimensions

27

Figure 3.3 - Short-term Tensile Testing Setup

28

PGT-A2-4

Longitudinal Strain (in./in.)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Longitudinal Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axi

al S

tress

(MP

a)

0

100

200

300

400

tLE =3.38x106 psi t

LF =56,959 psi

tLE =23.32 GPa t

LF =392.72 MPa

Figure 3.4 - Typical Tensile Coupon Stress-Strain Curve

29

3.2.2 Determination of Longitudinal Compressive Properties

In order to determine the longitudinal properties in compression, prismatic

coupons were cut to lengths that would ensure that material failure would occur before

buckling of the specimen. This length was determined using a simple stability analysis

(ASTM D3410):

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−≤ c

L

cL

LT

cL

g FE

GFtl 2.119069. (3.1)

where gl = coupon gage length t = coupon thickness c

LF = ultimate longitudinal compressive stress c

LE = longitudinal compressive modulus LTG = shear modulus This equation yields a conservative estimate of the buckling load for pinned end

constraints. For Equation 3.1, the ultimate longitudinal compressive stress and the

longitudinal compressive modulus were estimated using the results of the tension tests. It

was determined that the same size coupons from Scott and Zureick (1998) could

effectively be used in the current investigation. The nominal dimensions for the

compression coupons are given in Table 3.1 and a schematic illustration of the coupons

can be found in Figure 3.5.

A total of 18 uniaxial compression tests were performed in order to determine the

longitudinal compressive properties of the square tube sections used in this study. Three

different square tube sections were used with a specimen being cut from each of the four

panels. An additional section was cut from specimen A, from which two coupons were

cut to confirm the accuracy and repeatability of the test results. These specimens were

30

tested with the same boundary conditions that would later be used in the long-term creep

study. The samples were tested until failure and the ultimate stress was recorded. In

addition to these samples, four coupons were cut to the dimensions of the creep

specimens that were to be used in the long-term creep analysis. These specimens were 13

mm wider than those outlined in ASTM D3410. This was done in order to accurately

simulate the conditions found in the creep fixtures which were constructed for 38 mm

wide coupons. The dimensions of these specimens can be found in Table 3.1 and a

schematic illustration can be found in Figure 3.6. The specimens were equipped with a

single uniaxial extensometer that was removed at a predetermined stress of 138 MPa (20

ksi) to prevent damage of the extensometer. These additional tests were performed in

order to collect strain data to allow the stress-strain curves to be plotted and the

compressive modulus to be calculated. Due to the absence of the extensometer for the

remainder of the test, strain at failure was estimated based on an assumed linearity of the

stress-strain response of the composite material. A photograph of the short-term tensile

test setup can be found in Figure 3.7. A typical stress-strain diagram for the short-term

compressive coupon tests can be found in Figure 3.8 and all others can be found in

Appendix B. All longitudinal compression tests were performed using a hydraulic testing

machine and specimens without end tabs. Coupon preparation, loading procedure and

data reduction were performed in accordance with ASTM D3410 excluding the change in

width of the four coupons used for strain measurements.

31

25 mm

6.35 mm

127 mm

51 mm

Figure 3.5 - Nominal Compression Coupon Dimensions

32

38 mm

6.35 mm

127 mm

51 mm

Figure 3.6 - Nominal Compression Coupon Tested with Extensometer

Figure 3.7 - Short-term Compression Test Setup

33

PGC-C2-2

Longitudinal Strain, (in./in.)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Longitudinal Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axia

l Stre

ss, (

psi)

0

10000

20000

30000

40000

50000

60000

Axi

al S

tress

, (M

Pa)

0

100

200

300

400

cLE =3.86x106 psi c

LF =52,914 psi

cLE =26.66 GPa c

LF =364.8 MPa

Figure 3.8 - Typical Compression Coupon Stress-Strain Curve

34

3.2.3 Coupon Test Results

The following tables contain the dimensions of the coupons that were used and

the results of the short-term tensile and compressive coupon tests. The dimensions of the

coupons can be found in Table 3.2 and the results for each sample can be found in Tables

3.3 and 3.4. Average values for the longitudinal modulus (tension) ELt, longitudinal

modulus (compression) ELc, ultimate stress (tension) FL

t, and the ultimate stress

(compression) FLc can be found in Table 3.5. Short-term tests of the same material were

performed in previous works by Butz (1997) and Kang (2001). Thirty uniaxial

compression tests were performed by Butz and thirty uniaxial tensile tests were

performed by Kang. The values found in these studies are comparable to the values

found from short-term tests in the current investigation. The results of the current study

and these previous works can be found in Table 3.5.

35

Table 3.2 – Measured Coupon Dimensions

Specimen Thickness Width Area

mm in. mm in. mm2 in.2 Tension

PGT-A1-1 6.09 0.240 25.87 1.019 157.58 0.244 PGT-A1-2 6.26 0.246 25.81 1.016 161.54 0.250 PGT-A1-3 6.42 0.253 25.88 1.019 166.24 0.258 PGT-A1-4 6.41 0.253 25.78 1.015 165.36 0.256 PGT-A2-1 6.14 0.242 26.57 1.046 163.05 0.253 PGT-A2-2 6.27 0.247 25.92 1.020 162.45 0.252 PGT-A2-3 6.12 0.241 25.89 1.019 158.51 0.246 PGT-A2-4 6.16 0.242 25.96 1.022 159.89 0.248 PGT-C-1 6.21 0.245 25.35 0.998 157.55 0.244 PGT-C-2 6.29 0.248 25.24 0.994 158.84 0.246 PGT-C-3 6.35 0.250 25.32 0.997 160.74 0.249 PGT-C-4 6.12 0.241 25.08 0.987 153.42 0.238 PGT-D-1 6.14 0.242 25.36 0.999 155.62 0.241 PGT-D-2 6.41 0.252 25.40 1.000 162.80 0.252 PGT-D-3 6.29 0.248 25.28 0.995 158.95 0.246 PGT-D-4 6.19 0.244 25.36 0.998 157.01 0.243

Compression PGC-A1-1 6.17 0.243 25.50 1.004 157.40 0.244 PGC-A1-4 6.17 0.243 25.53 1.005 157.56 0.244 PGC-A2-1 6.02 0.237 25.37 0.999 152.75 0.237 PGC-A2-2 6.10 0.240 25.22 0.993 153.75 0.238 PGC-A2-3 6.38 0.251 24.79 0.976 158.05 0.245 PGC-A2-4 6.32 0.249 24.64 0.970 155.83 0.242 PGC-C1-1 6.27 0.247 25.45 1.002 159.67 0.247 PGC-C1-2 6.25 0.246 25.50 1.004 159.34 0.247 PGC-C1-3 6.68 0.263 25.40 1.000 169.68 0.263 PGC-C1-4 6.53 0.257 25.43 1.001 165.97 0.257 PGC-D1-1 6.30 0.248 25.48 1.003 160.48 0.249 PGC-D1-2 6.22 0.245 24.97 0.983 155.38 0.241 PGC-D1-3 6.30 0.248 25.22 0.993 158.88 0.246 PGC-D1-4 6.35 0.250 25.32 0.997 160.81 0.249 PGC-C2-1 6.02 0.237 38.10 1.50 229.4 0.356 PGC-C2-2 6.31 0.248 38.32 1.51 241.8 0.374 PGC-C2-3 6.29 0.247 38.43 1.51 241.7 0.373 PGC-A1-3 6.15 0.242 38.22 1.50 235 0.363

36

Table 3.3 – Results of Short-Term Tensile Tests

Tension

Specimen FLt EL

t

MPa psi GPa (10^3ksi)

PGT-A1-1* 314.55 45621 8.34 1.21

PGT-A1-2 384.39 55750 21.31 3.09

PGT-A1-3 361.19 52386 22.02 3.19

PGT-A1-4 417.69 60580 23.51 3.41

PGT-A2-1 350.62 50853 24.72 3.58

PGT-A2-2 413.41 59960 24.03 3.48

PGT-A2-3 365.85 53062 24.50 3.55

PGT-A2-4 392.72 56959 23.34 3.38

PGT-C-1 320.66 46508 21.89 3.17

PGT-C-2 332.69 48252 20.85 3.02

PGT-C-3 358.01 51924 21.45 3.11

PGT-C-4 396.22 57466 23.53 3.41

PGT-D-1 343.05 49755 20.23 2.93

PGT-D-2 448.36 65028 26.34 3.82

PGT-D-3 383.98 55691 21.83 3.16

PGT-D-4 382.99 55547 21.98 3.19

Average 376.79 54648 22.77 3.30

*Values were disregarded due to dramatic slipping of the extensometer

37

Table 3.4 – Results of Short-Term Compression Tests

Compression

Specimen FLc EL

c

MPa psi GPa (10^3ksi)

PGC-A1-1 384.47 55763 - -

PGC-A1-4 434.12 62963 - -

PGC-A2-1 316.97 45972 - -

PGC-A2-2 296.61 43020 - -

PGC-A2-3 384.95 55832 - -

PGC-A2-4 396.29 57477 - -

PGC-C1-1 355.32 51534 - -

PGC-C1-2 385.77 55951 - -

PGC-C1-3 458.77 66539 - -

PGC-C1-4 359.92 52202 - -

PGC-D1-1 329.74 47824 - -

PGC-D1-2 412.70 59857 - -

PGC-D1-3 358.41 51983 - -

PGC-D1-4 367.55 53309 - -

PGC-C2-1 324.60 47079 20.73 3.00

PGC-C2-2 364.83 52914 26.68 3.87

PGC-C2-3 334.53 48519 24.55 3.56

PGC-A1-3 289.08 41928 22.64 3.28

Average 364.15 52815 23.65 3.43

38

Table 3.5- Average Values from Short-Term Testing

FL EL

MPa psi GPa (10^3ksi)

Tension 376 54648 22.8 3.30

STD 34.4 4986 1.68 .244

C.O.V. 9.1% 7.4%

Compression 364 52815 23.7 3.43

STD 45.2 6557 2.55 .373

C.O.V. 12.4% 10.8% Tension

(Kang 2001) 372 54070 23.8 3.45

STD 25.6 3712 1.5 0.217

C.O.V. 6.9% 6.3% Compression (Butz 1997) 380 55114 23.8 3.46

STD 45.4 6583 0.96 .140

C.O.V. 12% 4%

3.3 Short-Term Elevated Temperature Tests

Compression tests were conducted at elevated temperatures to observe the effects

of temperature on the modulus of elasticity and the ultimate strength of the E-glass

polyester composite under short-term loading. Coupon specimens were tested in

compression at temperatures of 38°C (100°F), 54°C(130°F) and 65°C (150°F) until

failure. An environmental chamber was constructed on the base plate of a universal

testing machine that was capable of maintaining the desired temperatures. The chamber

was heated using a 450 watt finned strip heater and the temperature was regulated by a

remote bulb thermostat. Coupons were placed in the same fixture as used in the previous

compression tests. The coupons used for the elevated temperature tests were the same

39

dimensions as the previous compression tests with one notable exception; the length was

shortened from 127 mm (5 in.) to 114 mm (4.5 in.), which in turn shortened the gage

length from 51mm (2 in.) to 38 mm (1.5 in.). This reduction in length was based on the

stability Equation (3.1) and the expected reduction in modulus of elasticity at the higher

temperatures. The reduction in modulus was approximated using the manufacturer’s

design guidelines. The shortened sample ensured that the coupon would undergo

material failure rather than buckling. The coupons were equipped with strain gages and

tested until failure. The coupons were allowed to cure at their specified testing

temperature for 2 hours before the tests were started. This ensured that the heat was

completely distributed throughout the specimen. A picture of the environmental chamber

and test setup can be found in Figure 3.9. A typical stress-strain curve for each

temperature is shown in Figures 3.10 with all others appearing in Appendix B. The

results of all elevated temperature tests can be found in Table 3.6. The elevated

temperature tests showed appreciable reductions in both modulus of elasticity and

ultimate strength with increasing temperature. The percent reduction in these properties

from those found at room temperature can be found in Table 3.7.

40

Figure 3.9 – Test Setup for Short-Term Elevated Temperature Tests

41

Strain, in./in.

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Strain, mm/mm

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axia

l Stre

ss, p

si

0

10000

20000

30000

40000

50000

60000

Axi

al S

tress

, MP

a

0

100

200

300

400

65 Celsius54 Celsius38 Celsius

Figure 3.10 – Typical Stress-Strain Curves at Elevated Temperatures

42

Table 3.6 – Results of Short-Term Elevated Temperature Tests

Specimen Temp (°C) FL

c MPa (psi) εLc (mm/mm) EL

c GPa (ksi)

C1 65 233 (33737) 0.0118 20.9 (3032)

C2 54 301 (43708) 0.0134 22.4 (3256)

C3 38 361 (52423) 0.0175 20.6 (2987)

D1 65 195 (28335) 0.0100 19.5 (2828)

D2 54 364 (52746) 0.0158 23.0 (3329)

D3 54 240 (34825) 0.0129 18.6 (2695)

D4 38 342 (49691) 0.0132 25.9 (3758)

65°C Average 214 (31036) 0.0109 20.2 (2930)

54°C Average 302 (43760) 0.0140 21.3 (3093)

38°C Average 352 (51057) 0.0154 23.3 (3373)

23°C Average 364 (52815) 0.0140 23.65 (3430)

Table 3.7 – Reduction of Mechanical Properties Due to Temperature

Temperature % Reduction in FL

c % Reduction

in ELc

65°C Average 41.2 14.6

54°C Average 17.5 9.9

38°C Average 3.3 1.5

43

CHAPTER IV

LONG-TERM EXPERIMENTAL PROGRAM

4.1 Introduction

This chapter presents an investigation into the creep behavior of a pultruded E-

glass/polyester composite under sustained compressive loading and elevated

temperatures. The experiments were conducted at a stress level of 0.33 FLc and three

different temperatures. The temperatures investigated were 23.3°C (74°F), 37.7°C

(100°F), and 54.4°C (130°F). In addition to the tests conducted at these constant

temperatures, two tests were conducted under cyclic heating. All experiments were

performed for a minimum duration of 1,000 hours.

4.2 Specimen Details

The rectangular prismatic coupons used in this investigation were cut from the

panels of a 102 mm (4 in.) x 102 mm (4 in.) x 6.4 mm (0.25 in.) pultruded FRP square

tube. The gage length of the coupons was determined using the stability equation,

Equation (3.1), to prevent buckling and ensure compressive failure of the specimen. This

approach led to the specimen dimensions found in Table 4.1. It is notable that the coupon

gage length is shorter for the elevated temperature tests due to the expected decrease in

longitudinal modulus. This expected loss was based on the findings of the short-term

elevated temperature tests that were performed in this study. The specimen dimensions

can be seen in the schematic illustrations in Figures 4.1 and 4.2.

44

Table 4.1 – Nominal Coupon Dimensions for Creep Studies

Test Type t l lg b

mm in. mm in. mm in. mm in.

Room Temp. 6.35 0.25 127 5 51 2 38 1.5

Elevated Temp. 6.35 0.25 114 4.5 38 1.5 38 1.5

45

38 mm

6.35 mm

127 mm

51 mm

38 mm

6.35 mm

114 mm

38 mm

Figure 4.1 – Typical Room Temperature Creep Coupon

Figure 4.2 – Typical Elevated Temperature Creep Coupon

46

4.3 Long-Term Experimental Setup

The long-term experimental program utilized dead weight lever arm creep fixtures

to apply a compressive load to the coupons. A schematic of the creep fixtures can be

found in Figure 4.3. The fixture was constructed of structural steel and pillow block

roller bearings were used as the fulcrum for the lever arm. The dimension of the lever

arm allowed the dead weight load to be amplified by a factor of 10 on the coupons. The

cages in which the coupons were placed were designed to transfer the tensile load that

was placed on the fixture by the lever arm into compression on the coupons. Figure 4.4

shows a typical compression cage. Three such cages were placed inside each creep

fixture which allowed the simultaneous loading of three coupons with the same stress

level.

Two creep fixtures were outfitted to perform the elevated temperature tests. To

accomplish this, 38 mm (1.5 in.) thick fiberglass duct board insulation was cut and taped

around the outside of the creep fixture using foil tape to secure the corners and edges.

The rear of the creep fixture housed two 450 watt finned strip heaters which supplied the

heat to the chamber through an opening in the back of the heating chamber. Air was

circulated through the creep fixture using a high temperature blower. The blower

removed air from the top of the fixture and circulated it back through the chamber that

contained the heating strips for the air to be reheated. The temperature inside the

environmental chamber was monitored using a panel thermometer and regulated with a

remote bulb thermostat. Figure 4.5A shows a creep fixture without the environmental

chamber was assembled and Figure 4.5B shows the fixture after assembly.

47

Figure 4.3 – Schematic of Creep Fixture (from Scott and Zureick (1998))

48

Figure 4.4 – Typical Compression Cage (from Scott and Zureick (1998))

49

Figure 4.5A– (Left) Creep Fixture with Environmental Chamber

Figure 4.5B – (Right) Room Temperature Creep Fixture

A B

50

A stress level of 126MPa (18.3 ksi) was used for all creep tests. This value

represents approximately 33% of the ultimate stress that was determined in the short-term

testing. This percentage of the ultimate stress was chosen based on the manufacturer’s

design guidelines (Strongwell (1998)) in which a factor of safety of 3 is suggested for

structural elements in compression. This stress level also ensured that the test would be

conducted in the linear-elastic range of the material.

The three temperatures under investigation were 23.3°C (74°F), 37.7°C (100°F),

and 54.4°C (130°F). These temperatures were selected based on possible real world

applications of this material and the manufacturer guidelines. The manufacturer does not

recommend the use of this composite material above 65.5°C (150°F). The temperatures

that were selected are meant to reflect situations such as attics or crawlspaces which can

easily reach 54.4°C (130°F) in the summer months.

The coupons were inserted into the cage grips and aligned. After the coupons

were seated in the grips, concrete dead weights were added to reach the desired stress

level. The elevated temperature specimens were allowed 1 hour to acclimate to the

temperature before the concrete weights were applied. The specimen and cage

dimensions allowed for two specimens to be tested simultaneously at elevated

temperature.

Cyclically heated creep tests were performed at maximum temperatures of 37.7°C

(100°F), and 54.4°C (130°F). For these experiments the heat was applied for 8 hours and

then the heat was terminated for 16 hours. This was controlled using a timer which

controlled the power supply to the finned strip heaters. The load was applied to the

51

specimens at the beginning of the first heat cycle and the specimens were not allowed to

acclimate to the elevated temperature.

Figure 4.6 shows a creep fixture after the concrete weights have been applied.

Previous work by Scott and Zureick (1998) with the same creep fixtures showed that the

creep fixtures did not induce bending of the specimens. Therefore, the room temperature

coupons were equipped with a single uniaxial strain gage. Strain gages were used on

both sides of the elevated coupons to ensure that the elevated temperature did not induce

bending of the specimen. Strain readings for the room temperature coupons were based

on the previous work by Scott and Zureick (1998) and were recorded at the following

intervals:

Period 1: Once each six minutes (0.1 hours) for the first hour

Period 2: Once each 15 minutes for the next three hours

Period 3: Once each hour for the following 24 hours

Period 4: Once each day thereafter

The tests at elevated temperatures had periods that differed slightly and were as follows:

Period 1: Once each two minutes for the first hour

Period 2: Once each six minutes for the next hour

Period 3: Once each 15 minutes for the next three hours

Period 4: Once each hour for the next 24 hours

Period 5: Once each day thereafter

The specimen strain readings for each of the three temperatures and the cyclic heating are

shown in Figures 4.7, 4.8, 4.9, and 4.10.

52

Figure 4.6 – Creep Fixture with Applied Dead Load

53

Time, hours

0 500 1000 1500 2000 2500 3000

Cre

ep S

train

, με

0

100

200

300

400

500

600

Time, days

0 20 40 60 80 100 120

Specimen PGC-RT-1Specimen PGC-RT-2Specimen PGC-RT-3Findley Theory

Figure 4.7 – Creep Strains for Coupons at Room Temp. 23.3°C (74°F) and 0.33 FLc

54

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

1000

Time, days

0 10 20 30 40 50

Specimen PGC-100-1Specimen PGC-100-2AverageFindley Theory

Figure 4.8 – Creep Strains for Coupons at 37.7°C (100°F) and 0.33 FLc

55

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

1000

1200

1400

1600

Time, days

0 10 20 30 40 50

PGC-130-1Findley Theory

Figure 4.9 – Creep Strains for Coupons at 54.4°C (130°F) and 0.33 FLc

56

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

1000

1200

Time, days

0 10 20 30 40 50

Specimen PGC-100 CYC-1Specimen PGC-100 CYC-2Average 37.7oC Cyclic

Figure 4.10 – Creep Strains for Coupons under Cyclic Heating at 37.7°C (100°F) and 0.33 FL

c

57

4.4 Development of a Semi-Empirical Viscoelastic Model

The current investigation involved both time-dependent and temperature-

dependent behavior that needed to be incorporated into the viscoelastic model. Findley,

Lai, and Onaran (1976) asserted that the total strain ε under a given temperature T, and a

given stress f can be represented by:

tT εεε += (4.1)

where εt is the strain due to stress over time and εT is the tensor of thermal expansion.

Therefore the time-dependent and the temperature-dependent behavior could be modeled

separately and then summed to reach the total creep strain.

The time-dependent behavior of the material was modeled using the power law

developed by Findley (1944). This model provided an accurate model for the 26 year

creep data of an unreinforced thermoplastic material (Findley 1987). The Findley power

law also proved to be a good approximation for creep in a pultruded E-glass/vinylester

composite with a Vf of 30% (Scott and Zureick (1998)). As noted earlier, the material in

the current investigation had fiber volume fraction Vf of approximately 35% by volume.

Therefore, the creep deformation was assumed to be primarily matrix driven and as a

result the Findley power law would provide an accurate approximation of the data. The

simplest form of the Findley power law can be written as:

no mtt += εε )( (4.2)

where

ε(t) = total time-dependent strain

εo = stress-dependent initial elastic strain

m = stress-dependent and temperature-dependent coefficient

58

n = stress-independent and temperature independent material constant

t = time after loading

Since the total viscoelastic model has been separated into two distinct parts, time-

dependent behavior and temperature-dependent behavior, the room temperature creep

tests were used to model the time-dependent behavior only. Effectively, εT in Equation

(4.1) was considered to be zero and therefore the total strain was equal to the time-

dependent strain. The room temperature (23.3°C) model would serve as a reference for

the temperature-dependent studies. The empirical constants, m and n, needed to

formulate the power law can be found from the experimental creep data, rearranging

Equation (4.2) and taking the logarithm of both sides:

[ ] )log()log()(log tnmt o +=− εε (4.3)

Plotting Equation (4.3) on a log-log scale yields a straight line from which the empirical

constants can be calculated. From the resulting line, the y-intercept at t = 1 hour is

equivalent to the value of m and the slope of the line is the material constant n.

The creep strain data for the room temperature coupons are plotted on a

logarithmic scale in Figure 4.11. The values obtained for the constants m and n are given

in Table 4.2. The Findley models produced by these constants are plotted alongside the

experimental creep strain data in Figure 4.7. The power law model proved to be a good

approximation of the creep behavior of the E-glass/polyester material at room

temperature. Comparisons of n values from previous work can be found in Table 4.3.

59

Time, hours

1 10 100 1000 10000

Cre

ep S

train

, με

0.1

1

10

100

1000

Specimen PGC-RT-1Specimen PGC-RT-2Specimen PGC-RT-3

Figure 4.11 – Logarithmic Plot for Evaluation of Constants m and n at 23.3°C

60

Table 4.2 – Creep Constants m and n from Equation (4.3) at 0.33 FLc

and Room Temperature

Specimen εo (με)

m (με) n

PGC-RT-1 5339 129 .172

PGC-RT-2 5176 119 .181

PGC-RT-3 4854 116 .190

Average 5123 121 .183

Table 4.3 – Average values for the Material Constant n from Previous Works

Investigator Loading Regime n

McClure and Mohammadi (1995) Compression (Angles) 0.17

McClure and Mohammadi (1995) Compression 0.25

Scott and Zureick (1998) Compression 0.23

Current Investigation Compression 0.18

61

Using the average values of the empirical parameters m and n, the Findley power

law model using Equation (4.2) is equated to the time-dependent behavior of the material

that is currently been investigated. Due to the relationship shown in Equation (4.1), the

temperature-dependent behavior of the material can be found by subtracting the time-

dependent strains from the total strain recorded in the experimental data as follows:

tT εεε −= (4.4)

Using the results of Equation (4.4), a secondary Findley power law can be used to

express the temperature-dependent behavior of the material. To accomplish this, the

results of Equation (4.4) are found using the recorded strains at the elevated temperatures

as ε and the recorded strains at room temperature as εt. These results are then plotted on

a logarithmic scale and the values for m and n are taken in the same manner as described

earlier, where m is the y-intercept at t = 1 hour and n is the slope of the resulting straight

line. For the temperature-dependent model, these parameters will be designated as mT

and nT. The results from Equation (4.4) for the 37.7°C (100°F) and the 54.4°C (130°F)

experiments can be found in Figure 4.12 and the logarithmic plot can be found in Figure

4.13. Using the empirical constants mT and nT , given in Table 4.4, the temperature-

dependent creep strains can be modeled using a power law model where:

TnTo tmT += εε )( (4.5)

Thus, the strain as a function of time and temperature can be modeled by summing the

results of the room temperature and the temperature-dependent Findley power law

models:

62

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

1000

ε(t)37 - ε(t)23

ε(t)54 - ε(t)23

Figure 4.12 – Plot of Creep Strain at Elevated Temp., minus Creep Strain Measured at Room Temp.

63

Time, hours

1 10 100 1000 10000

Cre

ep S

train

, με

1

10

100

1000

10000

37.7 Celsius54.4 Celsius

Figure 4.13 – Logarithmic Plot of Creep Strain at Elevated Temp., minus Creep Strain Measured at Room Temp.

Table 4.4 –Constants mT and nT

Temperature mT nT

37.7°C (100°F) 231 0.0489

54.4°C (130°F) 635.7 0.0453

37.7°C (100°F) Cyclic 27.6 0.336

64

TRT nT

nRTo tmtmtT ++= εε ),( (4.6)

where

ε(T,t) = total time and temperature dependent strain

εo = stress-dependent initial elastic strain

mRT = stress-dependent and temperature-dependent coefficient at 23.3°C

nRT = stress independent material constant at 23.3°C

mT = stress and temperature-dependent coefficient at elevated temperature

nT = stress independent material constant at elevated temperature

t = time after loading

This model can be used to predict the strain response of the elevated temperature

specimens in the current study. Figure 4.14 shows the time and temperature dependent

model alongside the experimental creep data for all tests. It should be noted that the

initial elastic strains for all experiments were very similar and were found to be

independent of temperature for the range of temperatures in this study. Table 4.5 shows

the initial elastic strains for all coupons.

The same modeling procedure is also applicable to the cyclically heated

specimens as can be seen in Figure 4.15 which contains the experimental creep data and

the comprehensive model. The time and temperature dependent model was a very close

approximation of the creep data using the parameters mT and nT, found using the same

methods as the constant heat procedure. However, the parameters mT and nT did not

correlate with the parameters found from the constant heat experiments. Due to the

65

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

1000

1200

1400

23.3 Celsius37.7 Celsius54.4 CelsiusPower Law Model

Figure 4.14 – Experimental Creep Strain with Time/Temperature-Dependent Model

66

Table 4.5 – Initial Elastic Strains

Temperature (°C) Specimen εo (με) 23.3 1 5339 23.3 2 5176 23.3 3 4854 37.7 1 5157 37.7 2 4843 54.4 1 5195 54.4 2 4958

37.7 Cyclic 1 5376 37.7 Cyclic 2 4818

Average 5079 STD 216 COV 4.3%

67

Time, hours

0 200 400 600 800 1000 1200

Cre

ep S

train

, με

0

200

400

600

800

Time, days

0 10 20 30 40 50

Average 37.7oC CyclicPower Law Model37.7oC Constant

Figure 4.15 – 37.7°C Cyclic Heat Creep Strains with Power Law Model

68

greatly different values of mT and nT it was difficult to make comparisons between the

cyclically heated specimens and the constant heat experiments. The values of mT and nT

are shown in Table 4.4 for comparison. The 37.7°C (100°F) cyclically heated test

performed much as expected. The strain data is below the 37.7°C (100°F) constant heat

curve and increased slowly to approximately the same magnitude as the constant heat

test. This can be seen in Figure 4.15.

A creep test was performed under cyclic heat at 54.4°C (130°F) for comparison

with the 37.7°C (100°F) cyclic test in order to form an equation to predict the behavior of

cyclically heated specimens. However, the results were very erratic which can be

attributed to an error somewhere in the data acquisition process. Based on the strain

readings, the problem was most likely a cold solder joint where the lead wires were

attached to the strain gages or a pre-existing problem with the lead wires. This is

apparent due to the sporadic readings that were collected. A cold solder joint causes an

insufficient connection that can cause erratic readings due to small changes in the current

being passed through the strain gage.

As can be seen from Figure 4.15 the cyclic heating on the 37.7°C (100°F)

specimen caused a stair step effect in the strain values. The strain increased as the heat

was added and then decreased during a period of recovery when the heat was removed.

Figure 4.15 also indicates that the behavior of the cyclically heated specimens may

eventually converge with the behavior of the constant heat specimens. The strains

recorded in the later points are less influenced by temperature, which can be seen by the

smaller increases in strain during the heating cycles.

69

Equation (4.6) can be used to estimate the longitudinal strain over the possible

service life of the material as used in construction. The total creep strain can then be

compared to the short-term data to evaluate the possibility of material failure over a

structure’s service life. The predicted results may also be compared to the short-term

elevated temperature tests. Since total strains will be needed and the data revealed a

relatively consistent value for εo regardless of temperature, εo will be given a value of

5000 με for all temperature models. This value was established as the average

throughout all of the tests. Figure 4.16 shows the strain data extrapolated to 50 years.

Table 4.6 shows the increase in strain over the 50 year period. Table 4.7 shows the

comparisons between the predicted strains and the results of the short-term testing at both

room temperature and elevated temperature. As can be seen in Table 4.7, the total strain

approaches approximately half of the strain at failure seen in the short-term tests. In the

most extreme creep case, the 54.4°C (130°F) test, the strain was predicted to increase to

7,900 με after 50 years, which is just slightly more than half of the total strain at failure in

the short-term test. Under the stress level of 0.33 FLc, recommended by the

manufacturer, the total strain over a 50 year service life would not approach the short-

term ultimate strain. However, if the stress level was increased, the total strain could

easily approach the strain at failure in the short-term tests. These conclusions are

applicable only to the materials and temperatures used in the current investigation.

Further research is needed on a wider range of pultruded materials and environmental

conditions to assess the general applicability of creep models developed using Equation

(4.6).

70

Time, Hours

0 100000 200000 300000 400000 500000

Stra

in, μ

ε

4500

5000

5500

6000

6500

7000

7500

8000

Time, Years

0 10 20 30 40 50

23.3 Celsius37.7 Celsius54.4 Celsius

Figure 4.16 – Predicted Strains over a 50 Year Service Life

71

Table 4.6 – Increase in Longitudinal Strain over a 50 Year Service Life

23.3°C (Room

Temperature) 37.7°C 54.4°C

Time o

otTε

εε −),( o

otTε

εε −),( o

otTε

εε −),(

Years % % %

1 12.7 20.4 39.2

5 17.1 25.3 45.5

10 19.4 27.8 48.6

25 23.0 31.6 53.4

50 26.1 35.0 57.4

Table 4.7 – Comparison of Short-Term Strain Values with Creep Values

Temperature Strain (με)

23.3°C 16,600

37.7°C 15,400

54.4°C 14,000 Short-Term

(Strain at Failure)

65.6°C 10,900

23.3°C 6,300

37.7°C 6,700 Creep (50 years)

54.4°C 7,900

72

4.5 Time-Temperature Superposition Principle

Another approach to modeling the long-term performance of the FRP material is

to use the Time-Temperature Superposition Principle (TTSP) introduced in Chapter II.

The TTSP states that the effect of temperature on the time-dependent mechanical

behavior of the material is equivalent to a stretching of the real time for temperatures

above the given reference temperature (Findley, Lai, and Onaran (1976)), which in this

case is room temperature (23.3°C (74°F)). Since creep tests were performed at one stress

level and multiple temperatures above the reference temperature, a master curve can be

made by shifting the elevated temperatures curves using a modification factor. This

states that the following relationship exists:

),(),( ζεε oTtT = (4.7)

)(Ta

t

T

=ζ (4.8)

where

t = time after loading T = temperature To = reference temperature ζ = “reduced time” aT = shift factor The creep curves in the current study were only shifted horizontally; however, the TTSP

does allow for vertical shifts. The three creep curves from the current investigation are

plotted on a log-log scale in Figure 4.17. The data from the room temperature

(23°C(74°F)) test will be considered the reference temperature. The data for the room

temperature test extends to 2700 hours and a creep strain of 496 με. The time when the

73

Time, hours

1 10 100 1000 10000

Cre

ep S

train

, με

1

10

100

1000

10000

23.3oC37.7oC54.4oC

Figure 4.17 – Creep Strain for Temperature of 23.3°C, 37.7°C, and 54.4°C

74

specimen tested at 37.7°C (100°F) reached the same level of strain was identified from

the data as t ≈ 30 hours. Thus the data from the 37.7°C (100°F) test was shifted

horizontally at this point and joined to the reference temperature curve after the

appropriate shift factor was determined. The shift factor was determined by taking the

time that it took for the 37.7°C (100°F) test to reach 496 με and dividing it by the time for

the reference temperature to reach the same value. For this case it was:

0114.02700

8.30==Ta

After the determination of the shift factor each subsequent time interval between strain

readings was divided by the shift factor and added to the previous time starting at 2700

hours. The data from the 37.7°C (100°F) test was stretched to a time period of 88,190

hours (10.1 years). The results of this shift can be seen in Figure 4.18. The same

methodology was employed for the 54.4°C (130°F) curve. A strain value of 757 με was

determined to be the shift point of the 54.4°C (130°F) curve. The shift factor was

determined to be 5.273 x 10-5. This shift stretched the master curve to a time period of

2,165 years, which is far beyond any reasonable time duration. However, it did increase

the model beyond the 50 year service life, which is valuable for comparison with the

Findley power law model developed in Section 4.4. The results of this shift formed the

master curve which can be seen in Figure 4.19. A plot of the reciprocal of the shift

factors (logarithmic scale) versus (T-To) is given in Figure 4.20. The reference

temperature, To, was given a shift factor value of 1. The shift factors displayed a linear

increase with increasing temperature. A second master curve with a reference

temperature of 37.7°C (100°F) was also created using the same methodology and can be

seen in Figure 4.21.

75

Time, hours

1 10 100 1000 10000 100000 1000000

Cre

ep S

train

, με

1

10

100

1000

10000

Time, Years

0.001 0.01 0.1 1 10 100

Master Curve54.4oC

Figure 4.18 – Master Curve Including Shift of 37.7°C Curve

76

Time, hours

1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6 1e+7 1e+8

Cre

ep S

train

, με

10

100

1000

10000

Time, Years

0.001 0.01 0.1 1 10 100 1000 10000

Master Curve

Figure 4.19 – Master Curve for To (23.3°C) Including Shifts of Creep Data at 37.7°C an 54.4°C

77

T-To

0 10 20 30 40 50 60

1/a T

1

10

100

1000

10000

100000

oFoC

Figure 4.20 – Shift Factors for TTSP

78

Time, hours

1 10 100 1000 10000 100000 1000000

Cre

ep S

train

, με

1

10

100

1000

10000

Time, Years

0.001 0.01 0.1 1 10 100

37.7oC Master Curve

Figure 4.21 – Master Curve for To (37.7°C) Including Shift of Creep Data at 54.4°C

79

The Time-Temperature Superposition Principle applied to the data from the creep

tests in the current investigation was capable of modeling the time-dependent behavior of

the material well past the time period of interest for the 23.3°C (74°F) reference

temperature. The shifted curves formed reasonably smooth master curves from which

creep strain could be predicted for the reference temperatures, To, which were 23.3°C

(74°F) and 37.7°C (100°F) for this study. Comparisons of the predicted creep strains

from the TTSP and the semi-empirical Equation (4.6) can be seen in Table 4.8. The table

shows that the semi-empirical Findley model consistently predicted higher creep strain

values than the TTSP master curve. The difference between the two models increased

with the length of time predicted. The difference in the room temperature models can

possibly be attributed to physical aging of the elevated temperature specimens which is

not accounted for in the Findley model.

Table 4.8 – Predicted Strains for Material Using Two Methods

Time (Years)

23.3°C Semi-

Empirical Model

(με)

23.3°C TTSP (με)

% Diff.

37.7°C Semi-

Empirical Model

(με)

37.7°C TTSP (με)

% Diff.

1 638 558 12.5 997 1016 1.9

5 856 688 19.6 1244 1161 6.7

25 1148 895 22 1569 1253 20.1

50 1303 969 25.6 1740 N/A N/A

80

The Time-Temperature Superposition Principle can be used to characterize the

behavior of the material at 50 years utilizing shorter duration tests than the experiments

performed in the current study. The current study durations of 1,000 hours produced a

estimation of the creep strain over a period of 2,165 years. Analysis of the creep data in

this investigation reveals that three creep tests of 120 hours (5 days) would be sufficient

to provide an estimation of the strain response over a 50 year service life as shown in

Figures 4.22 and 4.23. Applying the TTSP to the measured data, the shorter testing

period yielded estimations of creep strain more consistent with the strains predicted by

the semi-empirical model, as shown in Table 4.9. Further research must be conducted in

order to confirm this test duration is sufficient for estimation of other materials.

81

Time, hours

1 10 100 1000

Cre

ep S

train

, με

1

10

100

1000

10000

23.3oC37.7oC54.4oC

Figure 4.22 - Recorded Creep Strain for 120 hours

82

Time, hours

1e+0 1e+1 1e+2 1e+3 1e+4 1e+5 1e+6

Cre

ep S

train

, με

1

10

100

1000

10000

Time, Years

0.001 0.01 0.1 1 10 100

23.3oC37.7oC54.4oC

50 yrs.

Figure 4.23 - TTSP Master Curve for Test Durations of 120 Hours, Allowing Prediction of Strain Response over a 50 Year Service Life

83

Table 4.9 – Predicted Strains Utilizing 120 Hour TTSP Curves and Semi-Empirical Model

Time (Years)

23.3°C Semi-Empirical

Model (με)

23.3°C TTSP (με)

% Diff.

1 638 568 11

5 856 893 4.3

25 1148 1085 5.5

50 1303 1118 14.2

84

4.6 Prediction of Time and Temperature Dependent Modulus

The constant mT in Equation (4.6) can be expressed as a hyperbolic function of

temperature as shown:

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ+⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ=⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ= ...

!31'sinh'

3

oooT T

TTTm

TTmm (4.9)

Substituting this into Equation (4.6) yields:

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ++=

o

nnRTo T

TtmtmtT TRT sinh'),( εε (4.10)

The parameters m’ and To are material constants determined from creep experiments at

various temperatures. The parameter ΔT is the temperature being modeled, T, minus the

material constant To. These material constants were determined from a plot of Equation

(4.9) as shown in Figure 4.24. The value of To was selected to ensure linearity and the

value of m’ was taken as the slope of the resulting line. From the curve To was

determined to be 23.3°C (74°F), which is equal to room temperature, and m’ was

determined to be 360 με for °C and 746 με for °F. Either temperature units may be used

as long as the correct value of m’ is used.

Previous work by Scott and Zureick (1998) provided a model for the time-

dependent modulus based on the material parameter m as a function of stress. The

current investigation extends this model to include the reduction in modulus due to

elevated temperatures. The original equation can be written as:

85

sinh(ΔΤ/Το)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

m (μ

ε)

0

100

200

300

400

500

600

700

Slope = m' = 749To = 74oF

Slope = m' = 360To = 23.3oC

Figure 4.24 – Evaluation of Creep Parameter m’ and To

86

n

t

oL

oL

L

tEEEtE

+=

1)( (4.11)

where

EL(t) = time-dependent longitudinal modulus of elasticity

ELo = initial elastic longitudinal modulus independent of time

Et = modulus which characterizes only the time-dependent behavior

n = stress independent material constant

t = time after loading (hours)

and

mfEt = (4.12)

where

f = applied stress

m = stress and temperature-dependent coefficient

For this investigation Equation (4.11) will be used to define the reduction in modulus of

elasticity over time and then extended to include the reduction due to temperature. The

material parameters mT and nT are substituted into Equations (4.11) and (4.12) to provide

an equation for the reduction in modulus due to temperature. When the parameters are

incorporated Equation (4.11) then becomes:

Tn

T

oL

oL

L

tEEETE

+=

1)( (4.13)

87

where

T

o

T mf

TTm

fE =

⎟⎟⎠

⎞⎜⎜⎝

⎛ Δ=

sinh' (4.14)

Therefore, the reduced modulus of elasticity due to time and temperature may be

expressed as:

))(())((),( tETEEtTE LLoLL Δ−Δ−= (4.15)

where

Tn

T

oL

oLo

LL

tEEEETE

+−=Δ

1)( (4.16)

and

n

t

oL

oLo

LL

tEEEEtE

+−=Δ

1)( (4.17)

Tables 4.10, 4.11 and 4.12 give predicted values of EL(T, t) for time periods of 1, 5, 10,

25, and 50 years. All predicted modulus values are based on a stress level of 0.33 FLc.

Figure 4.25 shows the total reduction in modulus values over a 50 year service period.

Equation (4.11) was used to predict the reduction in modulus for the 23.3°C (74°F)

coupons. Table 4.13 shows a comparison of modulus reduction at 50 years of service

life. The reduction in modulus of a similar material subjected to sustained loads at room

temperature (Scott and Zureick (1998)) is also included in Table 4.13.

88

Table 4.10- Predicted Modulus Reduction for Material at Room Temperature

23.3°C Average

ELo GPa (ksi) 23.1 (3345)

f MPa (ksi) 126 (18.333)

m (µε) 121

n 0.183

Et GPa (ksi) 1044 (151512)

Time (Years)

EL(t) GPa (ksi)

Decrease (%)

0 23.1 (3345) 0

1 20.7 (2997) 10.4

5 19.9 (2893) 13.5

10 19.6 (2842) 15.1

25 19.1 (2766) 17.3

50 18.6 (2702) 19.2

Table 4.11 – Predicted Modulus Reduction for Material at 37.7°C

37.7°C Average

ELo GPa (ksi) 23.1 (3345)

f MPa (ksi) 126 (18.333)

mT (µε) 268.55

nT 0.0391

ET GPa (ksi) 470.7 (68266)

Time (Years)

EL(T, t) GPa (ksi)

Decrease (%)

0 23.1 (3345) 0

1 19.2 (2778) 16.9

5 18.4 (2662) 20.4

10 18.0 (2604) 22.2

25 17.4 (2520) 24.7

50 16.9 (2450) 26.7

89

Table 4.12 – Predicted Modulus Reduction for Material at 54.4°C

54.4°C Average

ELo GPa (ksi) 23.1 (3345)

f MPa (ksi) 126 (18.333)

mT (µε) 622.34

nT 0.0453

ET GPa (ksi) 203.1 (29458)

Time (Years)

EL(T, t) GPa (ksi)

Decrease (%)

0 23.1 (3345) 0

1 17.3 (2507) 25.0

5 16.4 (2373) 29.1

10 15.9 (2307) 31.0

25 15.3 (2212) 33.9

50 14.7 (2134) 36.2

Table 4.l3 – Predicted 50 Year Reduction in Modulus

Investigation Stress Level Reduction in Modulus (50 years)

Scott and Zureick (1998) 0.40 FLc 21%

23.3°C (74°F) 0.33 FLc 19.2 %

37.7°C (100°F) 0.33 FLc 26.4 %

54.4°C (130°F) 0.33 FLc 35.8 %

90

Time, Years

0 10 20 30 40 50 60

E L(T,

t) /

Eo (

%)

50

60

70

80

90

100

110

23.3 Celsius37.7 Celsius54.4 Celsius

Figure 4.25 – Predicted Reduction in Modulus of Elasticity

Over a 50 Year Service Life

91

CHAPTER V

CONCLUSIONS AND PROPOSED DESIGN EQUATION

5.1 Conclusions

Based on the results of the short-term and long-term experimental program, the

following observations can be made:

1. The short-term elevated temperature tests performed at 37.7°C (100°F), 54.4°C

(130°F), and 65.6°C (150°F) revealed a noticeable decrease in the ultimate

strength and modulus of elasticity. The 65.6°C test showed a decrease in ultimate

strength of 43.5% and a decrease in modulus of 13%. These values are in general

agreement with the manufacturer’s design guidelines (STRONGWELL (1998)),

which predict a decrease of 50% in strength and 15% in modulus of elasticity for

the material subjected to a temperature of 65.6°C (150°F).

2. The Findley power law provides an accurate model of the creep performance of

the room temperature creep experiments. The power law modeled the strain in

the FRP material within 3.5% over a time duration of 2700 hours. All room

temperature creep tests yielded power law coefficients comparable to previous

work.

3. The time and temperature-dependent power law model provided a reasonably

accurate model of the creep strain in the pultruded FRP material for the time

duration studied. The temperature-dependent portion of the creep behavior could

be modeled using the Findley power law with the unique material parameters mT

and nT. The parameter mT could be expressed as a hyperbolic function of

temperature with an m’ value of 360 for temperatures given in degrees Celsius.

92

The value of m’ was 746 for temperatures given in degrees Fahrenheit. The value

used for To to ensure linearity of the plot of the parameter mT with temperature

was equal to room temperature, 23.3°C (74°F). This effectively made the

temperature-dependent portion of the power law model equal to zero at room

temperature, which was assumed early in the investigation. The values for nT

were very similar for both elevated temperature experiments and could be given a

value of 0.05 for practical use. Thus, the equation for the time and temperature-

dependent model could be expressed as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −++=

o

oo T

TTtmttT sinh'121),( 05.018.0εε (5.1)

where t is expressed in hours. This model can be used to predict the time-

dependent strain of the material under a given elevated temperature, T , and a

stress of 0.33 FLc.

4. The Time-Temperature Superposition Principle provided a reasonable model of

the long-term behavior of the material. Two master curves were made for the

23.3°C (74°F) and 37.7°C (100°F) specimens. The resulting predicted strain

values were reasonably close to the strain predicted by the Findley model for

shorter time periods of 1 to 5 years but diverged as the predicted time increased.

The TTSP model for the 37.7°C (100°F) specimen was closer to the results

predicted by the Findley model. The difference in the TTSP model and the

Findley model for the 23.3°C (74°F) case can possibly be attributed to physical

aging at the elevated temperatures used for the TTSP curve fitting. Analysis of

93

the creep data revealed that shorter creep test durations of 120 hours would be

sufficient to provide an estimation of the 50 year strain response of the material.

5. Equation (4.15) can be used to predict the reduction in modulus due to both time

and temperature. This equation is based on Equation (4.11) which was proposed

by Scott and Zureick (1998). Equation (4.15) incorporates the two temperature

parameters mT and nT to predict the reduction in modulus due to temperature.

5.2 Proposed Design Equation for the Time and Temperature-Dependent Modulus

Based on the data presented in this study, it is possible to formulate a design

equation that predicts the longitudinal elastic modulus EL(T, t) due to temperature and

time. This predictive equation can be achieved by simplifying Equations (4.15), (4.16),

and (4.17). This equation would allow the user to predict the modulus of elasticity at a

given temperature T and a stress level of 0.33 FLc, which is recommended by the

manufacturer, for the service life of the material.

For design purposes, it is more practical to have the time t in years rather than

hours. Rearranging Equation (4.15) yields:

oL

n

t

oL

oL

n

T

oL

oL

L Et

EE

E

tEE

EtTET

−

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+=

)8760(1)8760(1),( (5.2)

Due to the consistency of the room temperature creep tests for this material the empirical

parameter n can be given a conservative value of 0.20. The constant β oL

t

EE

= can be

94

introduced to further simplify the equation. The parameter nT can also be given a

conservative value of 0.05. This yields:

oL

oL

T

oL

oL

L Et

E

tE

EEtTE −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

+=

20.005.0 516.11),(

β

(5.3)

where

⎟⎟⎠

⎞⎜⎜⎝

⎛−

=1sinh'

o

T

TTm

fE (5.4)

For this work the stress level did not change, therefore the value of Et will remain the

same and can be calculated using Equation (4.12). If ELo is known then the constant β

can be calculated and used in Equation (5.3). Since the values of m’ and To for both

degrees Celsius and degrees Fahrenheit are known they can be used in Equation (5.4) to

develop equations for SI units and English units. The resulting equations may be written

as:

(SI) oL

oL

o

oL

L Et

E

tTT

EtTE −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=20.005.0

511sinh1.01),(

β

(5.5)

(Eng.) oL

oL

o

oL

L Et

E

tTT

EtTE −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=20.005.0

511sinh22.01),(

β

(5.6)

Further simplification of Equation (5.5) and (5.6) yields:

95

oLtTL EtTE ),(),( φ= (5.7)

where Φ(T,t) is a time and temperature dependent reduction factor given by:

(SI) 151

1

1sinh1.01

120.005.0

),( −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=tt

TT

o

tT

β

φ (5.8)

(Eng.) 151

1

1sinh22.01

120.005.0

),( −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=tt

TT

o

tT

β

φ (5.9)

For the current investigation β can be given a value of 45 for both Equations (5.8) and

(5.9). This value of β is determined based on the stress level of 0.33 FLc and the value of

ELo determined in the short-term material testing. The simplifications performed in the

earlier steps are meant to approximate the lower bound of the reduction in modulus while

at the same time simplifying the equation for design use. The results of the simplified

Equation (5.7) can be compared to the values found using Equation (5.2) in Figure 5.1. A

design example that utilizes the predictive equation for the modulus of elasticity can be

found in Appendix A.

It must be emphasized that this model is unique to the material, stress level, and

temperatures studied in the current investigation. Studies on other FRP materials at a

variety of stress levels and temperatures must be conducted in order to determine the

general applicability of the model.

96

Time, years

0 10 20 30 40 50 60

EL(

T,t)/

ELo (%

)

60

70

80

90

100

110

23.3 oC (Eq. 5.2)

37.7 oC (Eq. 5.254.4 o C (Eq. 5.2)Equation (5.7)(Design Eq.)

Figure 5.1 – Reduction in Modulus with Simplified Design Equation

97

5.3 Suggestions for Further Research

1. The 37.7°C (100°F) cyclically heated specimens yielded interesting results that

need additional research to further understand and model the creep behavior. The

behavior progressed as expected with the cyclically heated curve occurring below

the constant 37.7°C (100°F) curve. However, the cyclic data did approach the

same strain value as the constant heat curve after several hundred hours. Further

cyclically heated experiments performed at additional elevated temperatures

would allow an equation to be formulated to predict behavior under cyclic heat.

2. Additional research could include the variation of heat cycle durations. The

current study investigated durations of 8 hours which could be modified to be

longer or shorter to see the effect on the creep behavior.

3. Higher elevated temperatures could also be studied to see the effectiveness of the

model proposed in this study to predict temperatures outside of the

manufacturer’s suggested range. The investigation could determine the effective

range of the proposed model and how accurate it is within that range.

4. Multiple stress levels must also be investigated in order to observe the

applicability of the model to those stress levels. The parameter m could then

possibly be expressed as a function of both stress and temperature. Thus, yielding

a wider range of applicability of the model proposed in the current study.

5. Future studies could also incorporate the impact of moisture with elevated

temperatures, which is a combination often seen in the service life of a structure.

98

APPENDIX A

DESIGN EXAMPLE – LONG-TERM BEAM DEFLECTION

Check the adequacy of a unidirectionally reinforced pultruded wide flange

section, shown in Figure A1, for serviceability conditions for a 50 year service life in a

constant climate of 37.7°C (100°F). The beam is subjected to the loads as shown in

Figure A1. The initial deflection, the deflection due to time and temperature, and the

maximum deflection after 50 years must be in accordance with the EUROCOMP design

code (1996). The initial modulus of elasticity, ELo, of the member is determined from

coupon tests to be 23.1 GPa (3345 ksi) and the moment of inertia is 0.000792 m4 (1903

in4). The ultimate stress, FLc, is determined to be 186 MPa (27,000 psi). A maximum

deflection of L/250 is specified for general public access flooring. The design code also

specifies a limit state of L/300 for the time and temperature-dependent behavior after the

initial deflection without exceeding the maximum allowable deflection. Effectively:

Δmax – Δo = Δ(T,t) = L/300.

Solution:

Step 1: Determine limit states for beam deflection:

L/250 = 250

3 = .012 m = 12 mm (0.47 in.) = Δmax

L/300 = 300

3 = .010 m = 10 mm (0.39 in.) = Δ(T,t)

Step 2: Estimate initial deflection using classic beam theory:

Δo = )000792)(.1.23(384)3)(143(5

3845

4

44

mGPakN

EIwl

= = .0082 m = 8.2 mm

8.2 mm (0.32 in.) < 12 mm (0.47 in.)

99

3 m(9 .8 4 ft)

6 0 9 .6 m m(2 4 in )

1 9 0 .5 m m(7 .5 in )

9 .5 3 m m(3 / 8 in )

Y

Y

X X

w = 1 4 3 k N / m

1 9 .1 m m(3 / 4 in )

Figure A1 – Beam Deflection Example

100

Step 3: Determine the stress in the wide flange section

M = 8

)3)(143(8

22 kNwl= = 160,875 N-m (118 kip-ft)

f = 000792.

)3048)(.875,160(=

IMc = 62 MPa (9,000 psi)

18662

=tLFf = 33 % of ultimate strength*

* Proposed predictive modulus equation can be used

Step 4: Determine time and temperature-dependent modulus

oLtTL EtTE ),(),( φ=

151

1

1sinh1.01

120.005.0

),( −

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=tt

TT

o

tT

β

φ

150

4551

1

5013.237.37sinh1.01

120.005.0

),( −⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ −+

=tTφ

),( tTφ = 0.73

oLtTL EtTE ),(),( φ= = 0.73 (23.1 GPa) = 16.86 GPa (2,445 ksi)

Step 5: Determine deflection with reduced modulus

Δmax = )000792)(.9.16(384)3)(143(5

3845

4

44

mGPakN

EIwl

= = .0113 = 11.3 mm

11.3 mm (0.44 in) < 12 mm (0.47 in)

101

Step 6: Check deflection due to time and temperature dependent behavior with

serviceability conditions

Δmax – Δo = Δ(T,t) = 11.3 mm – 8.2 mm = 3.1 mm (0.12 in.)

3.1 mm (0.12 in.) < 10 mm (0.39 in.)

The design of the current beam satisfies the serviceability criteria proposed by the

EUROCOMP design guide. The beam satisfies these criteria for the initial deflection and

the maximum deflection after 50 years with time and temperature-dependent behavior

included. The design also satisfies the limit state for deflection due only to time and

temperature-dependent behavior.

102

APPENDIX B

STRESS VS. STRAIN CURVES FROM SHORT-TERM TESTING

103

SHORT-TERM TENSILE TESTS

Longitudinal Strain

0.00 0.01 0.02 0.03 0.04

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

Axia

l Stre

ss (M

pa)

0

100

200

300

Specimen PGT-A1-1

104

Longitudinal Strain

0.000 0.005 0.010 0.015 0.020

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A1-2

105

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axia

l Stre

ss (p

si)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A1-3

106

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axia

l Stre

ss (p

si)

0

10000

20000

30000

40000

50000

60000

70000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A1-4

107

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A2-1

108

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

70000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A2-2

109

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-A2-3

110

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

Axia

l Stre

ss (M

pa)

0

100

200

300

Specimen PGT-C1-1

111

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-C1-2

112

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-C1-3

113

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axia

l Stre

ss (p

si)

0

10000

20000

30000

40000

50000

60000

70000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-C1-4

114

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axia

l Stre

ss (p

si)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-D1-1

115

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

70000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-D1-2

116

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-D1-3

117

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGT-D1-4

118

SHORT-TERM COMPRESSION TESTS

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

Axia

l Stre

ss (M

pa)

0

100

200

300

Specimen PGC-C2-1

119

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGC-C2-3

120

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

Axia

l Stre

ss (M

pa)

0

100

200

300

Specimen PGC-A1-3

121

SHORT-TERM ELEVATED TEMPERATURE TESTS

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

Axia

l Stre

ss (M

pa)

0

50

100

150

200

250

Specimen PGC-C3-1at 65.6oC (150oF)

122

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

Axia

l Stre

ss (M

pa)

0

100

200

300

Specimen PGC-C3-2at 54.4oC (130oF)

123

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axia

l Stre

ss (p

si)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGC-C3-3at 37.7oC (100oF)

124

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012

Axia

l Stre

ss (p

si)

0

5000

10000

15000

20000

25000

30000

Axia

l Stre

ss (M

pa)

0

50

100

150

200

Specimen PGC-D2-1at 65.6oC (150oF)

125

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 0.020

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGC-D2-2at 54.4oC (130oF)

126

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

Axia

l Stre

ss (M

pa)

0

50

100

150

200

250

Specimen PGC-D2-3at 54.4oC (130oF)

127

Longitudinal Strain

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

Axi

al S

tress

(psi

)

0

10000

20000

30000

40000

50000

60000

Axia

l Stre

ss (M

pa)

0

100

200

300

400

Specimen PGC-D2-4at 37.7oC (100oF)

128

REFERENCES

ACI 440R-96 (1996), “State-of-the-Art Report of Fiber Reinforced Plastic (FRP) Reinforcement for Concrete Structures”, American Concrete Institute, Farmington Hills, MI., 68 pp. ASTM D3039/D3039M-93, Standard Test Methods for Tensile Properties of Polymer Matrix composite Materials, American Society for Testing and Materials ASTM D3410/D3410M-95, Standard Test Method for Compressive Properties of Polymer Matrix Composite Materials with Unsupported Gage Section by Shear Loading, American Society for Testing and Materials ASTM D638M (1996), “Standard Test Method for Tensile Properties of Plastics,” American Society for Testing and Materials International Bradley, S.W., Puckett, P.M., Baradley, W.L., and Sue, H.J. (1998), “Viscoelastic Creep Characteristics of Neat Thermosets and Thermosets Reinforced with E-glass”, Journal of Composites, Technology, and Research, Vol. 20, No. 1, pp. 51-58. Butz, T.M. (1997), Tests on Pultruded Square Tubes Under Eccentric Axial Load, M.S. Dissertation, Georgia Institute of Technology. Dutta, P.K. and Hui, D. (2000), “Creep Rupture of a GFRP Composite at Elevated Temperatures”, Computers and Structures, Vol. 76, No. 1-3, pp. 153-161 EUROCOMP (1996), Structural Design of Polymer Composites, Chapman and Hall, London, U.K., 751 pp. Findley, W.N. (1944), “Creep Characteristics of Plastics”, Symposium on Plastics, American Society for Testing and Materials, pp. 118-134. Findley, W.N., Worley, W.J. (1951), “The Elevated Temperature Creep and Fatigue Properties of a Polyester Glass Fabric Laminate”, Society of Plastic Engineers, Vol. V, No. 4, pp. 9-17. Findley, W.N., Lai, J.S., Onaran, K. (1976), Creep and Relaxation of Nonlinear Viscoelastic Materials, Dover Publications Inc., New York, NY. Findley, W.N. (1987), “26-Year Creep and Recovery of Poly(Vinyl Chloride) and Polyethylene”, Polymer Engineering and Science, Vol. 27, No. 8, pp. 582-585.

129

Gates, T.S. (1993), “Effects of Elevated Temperature on the Viscoplastic Modeling of Graphite/Polymeric Composites”, High Temperature and Environmental Effects on Polymeric Composites, ASTM STP 1174, pp. 201-221 Gibson, R.F., Hwang, S.J., Kathawate, G.R., Sheppard, C.H. (1991), “Measurement of Compressive Creep Behavior of Glass/PPS Composites Using the Frequency-Time Transformation Method”, International SAMPE Technical Conference, Vol. 23, pp. 208-218. Haj-Ali, Rami M., Muliana, Anastasia H. (2003), “A Micromechanical Constitutive Framework for the Nonlinear Viscoelastic Behavior of Pultruded Composite Materials”, International Journal of Solids and Structures, Vol. 40, No. 5, pp. 1037-1057. Kang, J.O. (2001), Fiber Reinforced Polymeric Pultruded Members Subjected to Sustained Loads, Ph. D. Dissertation, Georgia Institute of Technology. Katouzian, M., Brueller, O.S., Horoschenkoff, A. (1995), “Effect of Temperature on the Creep Behavior of Neat and Carbon Fiber Reinforced PEEK and Epoxy Resin”, Journal of Composite Materials, Vol. 29, No. 3, pp. 372-387. McClure, G. and Mohammadi, Y. (1995), “Compression Creep of Pultruded E-glass Reinforced Plastic Angles”, Journal of Materials in Civil Engineering, Vol. 7, No. 4 pp. 269-276. Papanicolaou, G.C., Zaoutsos, S.P., Cardon, A.H. (1999), “Further Development of a Data Reduction Method for the Nonlinear Viscoelastic Characterization of FRPs”, Composites- Part A: Applied Science and manufacturing, Vol. 30, No. 7, pp 839-848. Raghavan, J., Meshii, M. (1997), “Creep of Polymer Composites”, Composite Science and Technology, Vol. 57, No. 12, pp. 1673-1688. Raghavan, J., Meshii, M. (1997), “Creep Rupture of Polymer Composites”, Composite Science and Technology, Vol. 57, No. 4, pp. 375-388 Saadatmanesh, Hamid (1999), “Long-Term Behavior of Aramid Fiber Reinforced Plastic (AFRP) Tendons”, ACI Materials Journal, Vol. 96, No. 3, pp. 297-305. Scott, D.W., Zureick, A. (1998), “Creep behavior of Fiber-Reinforced Polymeric Composites: A Review of the Technical Literature”, Journal of Reinforced Plastics and Composites, Vol. 14, pp. 588-617. Scott, D.W., Zureick, A. (1998), “Compression Creep of a Pultruded E-glass/Vinylester Composite”, Composites Science and Technology, Vol. 58, No. 8, pp. 1361-1369.

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Spence, Brian R. (1990), “Compressive Viscoelastic Effects (Creep) of a Unidirectional Glass/Epoxy Composite Material”, National SAMPE Symposium and Exhibition (Proceedings), Vol. 35, No. 2, pp. 1490-1493. STRONGWELL (2002), Extren Design Manual, Strongwell Corporation, Vristol, VA. Tuttle, M.E., Brinson, H.F. (1986), “Prediction of the Long-Term Creep Compliance of General Composite Laminates”, Experimental Mechanics, Vol. 26, No. 1, pp. 89-102. Wang, Youjiang and Zureick, A.H. (1994), “Characterization of the Longitudinal Tensile Behavior of Pultruded I-shape Structural Members Using Coupon Specimens”, Composite Structures, Vol. 29, No. 4, pp. 463-472. Wen, V.F., Gibson, R.F., Sullivan, J.L. (1995), “Characterization of Creep Behavior of Polymer Composites by the use of Dynamic Test Methods”, American Society of Mechanical Engineers, Noise Control and Acoustics Division, Vol. 20, pp. 383-396. Yen, Shing-Chung, Williamson, Fay L. (1990), “Accelerated Characterization of Creep Response of an Off-Axis Composite Material”, Composites Science and Technology, Vol. 38, No. 2, pp. 103-118.